Anyone clicking on the following link before February 10, 2018, will be taken directly to the final version of the article [177]

** Modelling and Computing Homotopy Types: I**

on ScienceDirect. No sign up, registration or fees are required; they can simply click and read.

last updated, January 7, 2018

In 2013, Ronald Brown had 124 items on MathSciNet and was cited 998 times by 456 authors in the MR Citation Database.

This page contains a number of links to pdf and other files.

Preprint page

Nonabelian Algebraic Topology :

filtered spaces, crossed complexes, cubical homotopy groupoids by Ronald Brown,
Philip J. Higgins, Rafael Sivera (description
of new book: xxxv+668 pages, full pdf downloadable as hyperref
e-book; EMS Tract vol 15,
ISBN 978-3-13719-083-8, August 2011).

This gives a new foundation for algebraic
topology, relying on a Seifert-van Kampen Theorem for the fundamental
crossed complex of a filtered space, which allows new proofs of some classical
theorems such as the Relative Hurewicz Theorem; it also allows new calculations
of some nonabelian second relative homotopy
groups, not available by traditional methods of singular homology
and simplicial approximation. Indeed, it allows computation of some homotopy
2-types, based on calculations with crossed modules. Dealing with algebraic
models of homotopy types requires a different approach to algebraic topology
than the classical one.

Higher dimensional group theory web article started 1996

Nonabelian tensor product of groups : this is a link to a bibliography of 161 items on this topic, initiated in items [42] and [51].

Articles on Popularisation and Teaching

Mathematics and Knots: click here to see the sculptures of John Robinson and the exhibition Mathematics and Knots.

Ronald Brown PUBLICATIONS

DPhil Thesis: `Some problems in algebraic topology: a study of function space,
function complexes, and FD-complexes' Submitted December, 1961, 140 pages.
Part A, prelims, p. 1-28. 10.5MB

This Part contains the work on the cartesian closed category of Hausdorff
k-spaces developed in [1,2], and also a brief exposition on what are now
called monoidal closed categories.

a. Elements of Modern Topology, McGraw Hill, Maidenhead, 1968 (out of print
in 1972).

b. (coedited with T.L. Thickstun), Low-Dimensional Topology, (Volume 1 of
the conference on Topology in Low Dimension, Bangor 1979), London Math. Soc.
Lecture Notes No. 48 (1982). (this is now available again from CUP).

c. Topology: a geometric account of general topology, homotopy types, and
the fundamental groupoid, Ellis Horwood, Chichester (1988) 460 pp. revised
edition of (a). (out of print in 1992).

d. Topology and
Groupoids, Booksurge PLC, 2006, revised
and updated edition of (c).

e. Nonabelian algebraic topology, with P.J.
Higgins and R. Sivera (in press), EMS Tracts in Mathematics, vol 15, 703 pages.

(i) ``How mathematics gets into knots'', London Mathematical Society Popular
Lectures Video Series, (1987) 50 min.

(ii) ``Mathematics and knots'', Exhibition of 16 A2 boards, designed by R.Brown,
N.D.Gilbert, and T.Porter, Mathematics and Knots, Bangor, 1989. Exhibited
at the Royal Society/ Joint Mathematical Council Pop Maths Roadshow, 1989-90;
British Association for the Advancement of Science, Swansea, 1990; National
Science Festival, Edinburgh, 1994.

(iii) ``Pivoted lines and the M\"obius Band'', Computer Graphics Video,
Storyline by R. Brown, Programming by Ramen Sen, Mathematics and Knots /
IBM UK 4min. (1992). See the end of Pivoted lines and the Möbius Band.

(iv) ``Symbolic Sculptures and Mathematics'',
Symbolic Sculptures and Mathematics

Sculptures: John Robinson. Production: Cara Quinton. Mathematics: Ronald
Brown. Edition Limitée; Centre for the Popularisation of Mathematics,
1996.

(v)Web Site
Knot Exhibition
Centre for the Popularisation of
Mathematics, 1997.

(vi) `Raising public awareness of mathematics': This was a CDRom published for World Mathematics Year 2000 and funded by the EC.
It is largely incorporated in this web site .

1.
``Ten topologies for 𝑿× 𝒀'',
— Quart. J. Math. (2) 14 (1963), 303-319.
pdf

2.
``Function spaces and product
topologies'', — Quart. J. Math. (2) 15 (1964), 238-250.
pdf

3. ``Cohomology with chains as coefficients'', — Proc. London
Math. Soc. (3) 14 (1964), 545-565.
pdf file

4. ``On Künneth suspensions'', — Proc. Camb. Phil. Soc.
60 (1964) 713-720. pdf

5.
``The twisted Eilenberg-Zilber theorem'',
— Celebrazioni Archimedi de secolo xx, Syracusa, 1964, Simposi di topologia
(1967) 33-37. pdf

6.
``On a method of P. Olum'', — J.
London Math. Soc. 40 (1965), 303-304. pdf

7. ``Two examples in homotopy theory'', — Proc. Camb. Phil.
Soc. 621 (1966) 575-576. pdf

8.
``Groupoids and Van Kampen's theorem'',
— Proc. London Math. Soc. (3) 17 (1967)
385-401. pdf

9. (with P.R. HEATH), ``Coglueing homotopy equivalences'', —
Math. Z. 113 (1970) 313-362. pdf

10.
``Fibrations of groupoids'', —
J. Algebra 15 (1970) 103-132. pdf
7.6MB

10a.
``The calculus and modern mathematics'',
— Mathematics Teaching 51 (1970) 6pp.

11.
``Groupoids as coefficients'', —
Proc. London Math Soc. (3) 25 (1972) 413-426.
pdf file

12.
``Sequentially proper maps and a
sequential compactification'', — J. London Math Soc. (2) 7 (1973) 515-522.
pdf file

13. (with G. DANESH-NARUIE), ``The fundamental groupoid as a
topological groupoid'', — Proc. Edinburgh Math. Soc. 19 (1975) 237-244.
pdf

14.
(with J.P.L. HARDY), ``Subgroups of
free topological groups and free topological products of topological groups'',
— J. London Math Soc. (2) 10 (1975) 431-440.
pdf

15.
(with P.J. HIGGINS and S.A. MORRIS),
``Countable products of lines and circles: their closed subgroups, quotients
and duality properties'', — Math. Proc. Camb. Phil. Soc. 78 (1975) 19-32.
pdf

16. ``Some non-projective subgroups of free topological groups'',
— Proc. Amer. Math. Soc. 52 (1975)
443-440. pdf

17.
(with J.P.L. HARDY and S.A. MORRIS),
``The homotopy groups of an 𝒏-fold wedge'', — Math. Z. 143 (1975) 119-121.

18.
(with J.P.L. HARDY), ``Topological
groupoids I: universal constructions'', — Math. Nachr. 71 (1976)
273-286. pdf

19.
(with G. DANESH-NARUIE and J.P.L.
HARDY), ``Topological groupoids II: covering morphisms and 𝑮-spaces'',
— Math. Nachr. 74 (1976) 143-156. pdf

20. (with C.B. SPENCER), `` 𝑮-groupoids, crossed modules
and the fundamental groupoid of a topological group'', — Proc. Kon. Ned.
Akad. v. Wet. 7 (1976) 296-302.
pdf

21. (with C.B. SPENCER), ``Double groupoids and crossed modules'',
Cah. Top. Géom. Diff. 17 (1976) 343-362.
pdf
pdferratum

22.
(with P.J. HIGGINS), ``Sur les complexes
croisés, ω-groupoïdes et 𝑻-complexes'', — C.R. Acad. Sci.
Paris Sér. A. 285 (1977) 997-999.
pdf

23. (with P.J. HIGGINS), ``Sur les complexes croisés d'homotopie
associés a quelques espaces filtrés'', — C.R. Acad. Sci. Paris Sér.
A.286 (1978) 91-93.
pdf

24.
(with S.A. Morris), ``Embeddings in
contractible or compact objects'', — Coll. Math. 38 (1978) 193-212.
pdf

25.
(with P.J. HIGGINS), ``On the connection
between the second relative homotopy groups of some related spaces'', —
Proc. London Math. Soc. (3) 36 (1978) 193-212.
pdf file

26.
(with P.I. BOOTH), ``Spaces of partial
maps, fibred mapping spaces and the compact-open topology'', — Gen. Top.
Appl. 8 (1978) 181-195. pdf

27.
(with P.I. BOOTH), ``On the application
of fibred mapping spaces to exponential laws for bundles, ex-spaces and other
categories of maps'', — Gen. Top. Appl. 8 (1978) 165-179.
pdf

28.
(with P. NICKOLAS), ``Exponential
laws for topological categories, groupoids and groups and mapping spaces
of colimits'', — Cah. Top. Géom. Diff. 20 (1979)
179-198. pdf

29.
(with A.M. ABD-ALLAH), ``A compact-open
topology on partial maps with open domain'', — J. London Math Soc. (2)
21 (1980) 480-486. pdf

30.
``On the second relative homotopy
group of an adjunction space: an exposition of a theorem of J.H.C. Whitehead'',
— J. London Math. Soc. (2) 22 (1980) 146-152.
pdf

31. (with P.J. HIGGINS), ``On the algebra of
cubes'', — J. Pure Appl. Algebra 21 (1981) 233-260.
pdf

32. (with P.J. HIGGINS), ``Colimit theorems
for relative homotopy groups'', — J. Pure Appl. Algebra 22 (1981) 11-41.
pdf

33.
(with P.J. HIGGINS), ``The equivalence
of Ω-groupoids and cubical Τ-complexes'', — Cah. Top. Géom.
Diff. 22 (1981) 349-370.
pdf

34.
(with P.J. HIGGINS), ``The equivalence
of ∞-groupoids and crossed complexes'', — Cah. Top. Géom. Diff.
22 (1981) 371-386.
pdf

35. (with J. HUEBSCHMANN), ``Identities among relations'', in —
Low dimensional topology, London Math. Soc. Lecture Note Series 48 (ed.
R. Brown and T.L. Thickstun, Cambridge University Press, 1982), pp. 153-202.
pdf 8MB

36.
``Higher dimensional group theory'',
in — Low dimensional topology, London Math Soc. Lecture Note Series 48
(ed. R. Brown and T.L. Thickstun, Cambridge University Press, 1982), pp.
215-238.

37.
(with P.J. HIGGINS), ``Crossed complexes
and non-abelian extensions'', — Category theory proceedings, Gummersbach,
1981, Lecture Notes in Math. 962 (ed. K.H. Kamps et al, Springer, Berlin,
1982), pp. 39-50. pdf
(6.1MB)

38. ``Non-abelian cohomology and the homotopy classification of
maps'', in — Homotopie algébrique et algebre locale, Conf. Marseille-Luminy
1982, ed. J.-M. Lemaire et J.-C. Thomas, Astérisques 113-114 (1984), 167-172.
pdf (1.2MB)

39. ``An introduction to simplicial Τ-complexes'', in — Esquisses
Math., 32 (1982) 1-27.
pdf (2.4MB)

40.
(with P.R. HEATH and H. KAMPS),
``Groupoids and the Mayer-Vietoris sequence'', — J. Pure Appl. Alg. 30
(1983) 109-129. pdf (4.3MB)

41. (with A. RAZAK), ``A van Kampen theorem for unions of non-connected
spaces'', — Archiv. Math. 42 (1984) 85-88.
pdf

42. (with J.-L. LODAY), ``Excision homotopique en basse dimension'',
— C.R. Acad. Sci. Paris Sér. I 298 (1984) 353-356.
pdf

43.
``Coproducts of crossed Ρ-modules:
applications to second homotopy groups and to the homology of groups'', —
Topology 23 (1984) 337-345. pdf

44. (with P.R. HEATH and K.H. KAMPS), ``Coverings of groupoids
and Mayer-Vietoris type sequences'', — Categorical Topology, Proc. Conf.
Toledo, Ohio, 1983. (Heldermann Verlag, Berlin) (1984)
147-162. pdf

45. ``Some non-abelian methods in homotopy theory and homological
algebra'', — Categorical topology: Proc. Conference Toledo, Ohio, 1983,
(ed. H.L. Bentley et al., Heldermann, Berlin, 1984), pp. 108-146.

46.
(with S.P. HUMPHRIES), ``Orbits under
symplectic transvections I'', — Proc. London Math. Soc. (3) 52 (1986)
517-531. pdf file 3.2MB

47.
(with S.P. HUMPHRIES), ``Orbits under
symplectic transvections II: the case 𝑲= 𝔽_{2}'', — Proc. London Math.
Soc. (3) 52 (1986) 532-556. pdf
file

48. (with P.J. HIGGINS), ``Tensor products and homotopies for
ω-groupoids and crossed complexes'', — J. Pure Appl. Alg. 47 (1987)
1-33.
pdf

49. (with J.-L. LODAY), ``Homotopical excision, and Hurewicz theorems,
for 𝒏-cubes of spaces'', — Proc. London Math. Soc. (3) 54 (1987) 176-192.
pdf

50.
``From groups to groupoids: a brief
survey'', — Bull. London Math. Soc. 19 (1987) 113-134.
pdf

51.
(with J.-L. LODAY), ``Van Kampen theorems
for diagrams of spaces'', — Topology 26 (1987) 311-334.
pdf

52.
(with D.L. JOHNSON and E.F. ROBERTSON),
``Some computations of non-abelian tensor products of groups'', — J. Algebra
111 (1987) 177-202.
pdf

53.
(with P.R. HEATH), ``Lifting amalgamated
sums and other colimits of groups and topological groups'', — Math. Proc.
Camb. Phil. Soc. 102 (1987) 273-280.

54.
``A non abelian tensor product of
groups'', — Algebra-Tagung Halle 1986, Wissensch. Beitr., 33, Martin-Luther
Univ. Halle-Wittenberg, Halle-Saale, (1987) 59-72.

55.(with G.J. ELLIS), ``Hopf formulae for the higher homology
of a group'', — Bull. London Math. Soc. 20 (1988) 124-128.
pdf
erratum

56.
``Carpentry: a fable'', — Mathematical
Intelligencer, 11, no.4 (1989) 37.
html

57.
(with M. GOLASINSKI), ``A model structure
for the homotopy theory of crossed complexes'', — Cah. Top. Géom. Diff.
Cat. 30 (1989) 61-82.
pdf

58.
``Symmetry, groupoids, and higher
dimensional analogues'', — Symmetry II, ed. Istvan Hargittai, — Computers
Math. Applic. 17 (1989) 49-57.

59. (with N.D. GILBERT), ``Algebraic models of 3-types and automorphism
structures for crossed modules'', — Proc. London Math. Soc. (3) 59 (1989)
51-73. pdf file

60.
``Triadic Van Kampen theorems and
Hurewicz theorems'', — Algebraic Topology, Proc. Int. Conf. March 1988,
Edited M.Mahowald and S.Priddy, Cont. Math. 96 (1989) 39-57.
pdf 5.5MB pdf .3MB revised

61.
(with P.J. HIGGINS), ``Crossed complexes
and chain complexes with operators'', — Math. Proc. Camb. Phil. Soc.
107 (1990) 33-57.
pdf

62. ``Some problems in non-Abelian homotopical and homological
algebra'', — Homotopy theory and related topics, Proceedings Kinosaki,
1988, ed. M. Mimura, Springer Lecture Notes in Math., 1418 (1990) 105-129.
pdf

63.
``Conversations with John Robinson''
in — Symbolism: sculptures and tapestries, by John Robinson, (Mathematics
and Knots, Bangor, Wales) (1989) 2-29. pdf

64.
``Why we made an exhibition'', in
— Souvenir Guide to the Pop Maths Road Show, Royal Society/ Joint Mathematics
Council (1989) 10-12.

65.
(with T.PORTER), ``Making a mathematical
exhibition'', in — The popularization of mathematics, edited A.G.Howson
and J.-P. Kahane, ICMI Study Series, Cambridge University Press, (1990) 51-64.
see
icmi89.html

66. Review of — Algebraic homotopy, by H.J.Baues, Cambridge
University Press, 1988, 455pp, — Bull.American Math. Soc. 23 (1990) 182-190.

67. (with T.PORTER), ``Mathematics in Context: a new course'',
— For the Learning of Mathematics, 10 (1990) 10-15.

68.
``𝒒-perfect groups and universal
𝒒-central extensions'', — Publ. Mat. Univ. Auton. Barcelona 34 (1990)
291-297. pdf

69. ``Local-to-global techniques, groupoids, and holonomy'', —
Proceedings International Conference on the Calculus of Variations, Tbilisi
Nov. 1989.

70.
``Higher order symmetry'', — Proc.
of Assiut First International Conference of Mathematics and Statistics, Assiut,
Feb, 1990, Part I, Algebra and Geometry, Ed. E.K.Al-Hussaini and
A.M.Abou-El-Ela, University of Assiut, (1990), 25-44.

71. (with P.J.HIGGINS), ``The classifying space of a crossed complex'',
— Math. Proc. Camb. Phil. Soc. 110 (1991) 95-120.
pdf

72. (with H.J.BAUES), ``On the relative homotopy groups of the
product filtration and a formula of Hopf'', — J. Pure Appl. Algebra 89
(1993) 49-61.
pdf

73.
Preface to — Combinatorial homotopy
and four-dimensional complexes, by H.J.Baues, pp x-xx, de Gruyter, Berlin,
1991.

74. ``Computing homotopy types using crossed 𝒏-cubes of groups'',
— Adams Memorial Symposium on Algebraic Topology, Vol 1, edited N. Ray
and G Walker, Cambridge University Press, 1992, 187-210.
pdf

75.
(with M. E.-S. A.-F. AOF), ``The holonomy
groupoid of a locally topological groupoid'', — Top. Appl., 47 (1992)
97-113.
pdf

76.
(with K.C.H.MACKENZIE), ``Determination
of a double Lie groupoid by its core diagram'', — J. Pure Appl. Algebra,
80 (1992) 237-272. pdf

77.
(with JOHN ROBINSON), ``Borromean
circles'', — Letter, American Math. Monthly, April, (1992) 376-377.

78. ``Out of line'', — Royal Institution Proceedings, 64 (1992)
207-243.
pdf
html

79.
(with J.ROBINSON), ``The Universe
Series of Symbolic Sculptures'', in — Symbolic Sculptures, by John Robinson,
Edition Limiteé, Carouge Geneve, (1992), 103-123.

80.
``The Waldegrave White Paper'', —
London Math. Soc. Newsletter, November, (1992).

81. (with T. PORTER), ``Why choose mathematics?'', in — Mathematics
for the Future, IMA and Hobson's Press, 1993, 1994, 1995).

82. (with O. MUCUK), ``Covering groups of non-connected topological
groups revisited'', — Math. Proc. Camb. Phil. Soc, 115 (1994) 97-110.
pdf

83. (with C.PRITCHARD), ``The third man's knotty problems'', —
The Scottish Mathematical Council Journal, 23 (1993) 62-66. pdf

84.
``Symbolic sculptures by John Robinson",
— Bangor Tourist Guide, Mathematics and Knots, 1993.

85. ``Higher order symmetry of graphs'', — Bull. Irish Math.
Soc. 32 (1994) 46-59.
pdf

86. (with A.P.TONKS), ``Calculations with simplicial and cubical
groups in AXIOM'', — J. Symbolic Computation, 17 (1994) 159-179.

87. (with T.PORTER), ``The methodology of mathematics'', — Bulletin
International Commission of Mathematical Instruction, 37 (1994) 23-37.

88. (with O. MUCUK), ``The monodromy groupoid of a Lie groupoid'',
— Cah. Top. Géom. Diff. Cat,36 (1995) 345-369.
pdf

89.
(with O. MUCUK), ``Foliations, locally
Lie groupoids, and holonomy'', — Cah. Top. Géom. Diff. Cat, 37 (1996)
61-71. pdf

90.
(with T. PORTER),
``The methodology
of mathematics'', — Math. Gazette,
79, July (1995) 321-334. — CUBO 2 (2000) 85-100.

91.
``Representation and computation for
crossed modules'', Proceedings — Catégories, Algebres, Esquisses,
Neo-esquisses, Caen, 1994, 6pp.

92.
(with C.D.WENSLEY), ``On finite induced
crossed modules and the homotopy 2-type of mapping cones'', — Theory and
Applications of Categories 1(3) (1995) 54-71.pdf

93.
``Homotopy theory, and change of base
for groupoids and multiple groupoids'', — Applied categorical structures,
4 (1996) 175-193.
pdf

94.
(with M. GOLASINSKI, T.PORTER and
A.P.TONKS), ``Spaces of maps into classifying spaces for equivariant crossed
complexes,'' — Indag. Mathem., 8 (1997) 157-172.
pdf
pdfcorr

95.
(with C.D.WENSLEY), ``Computing crossed
modules induced by an inclusion of a normal subgroup, with applications to
homotopy 2-types'', — Theory and Applications of Categories 2 (1996)
3-16. pdf

96.
(with G.JANELIDZE), ``Van Kampen theorems
for categories of covering morphisms in lextensive categories'', — J.
Pure Appl. Algebra 119 (1997) 255-263. pdf

97. (with T. PORTER), ``On the Schreier theory of non-abelian
extensions: generalisations and computations'', — Proceedings Royal Irish
Academy, 96 (1996) 213-227. pdf

98.
(with G.JANELIDZE), "Galois theory
of second order covering maps of simplicial sets", J. Pure Applied Algebra,
135 (1999) 83-91.pdf

99.
`What should be the output of mathematical
education??', in — Mathematics Education
as a research domain: a search for identity, edited Kilpatrick, J., Sierpinska,
A., Kluwer, Lancaster, 1997, 459-476.pdf

100. (with T.PORTER), "Matematikos metodologia", Alfa + Omega, 1
Nr 5 (1998) 71-84 (Lithuanian translation of `The Methodology of Mathematics',
Formally, "Alpha+omega" is a supplement of the "Lithuanian Mathematical Journal",
which has an ISSN number 0132--2818.)

101.
`Mathematics and knots', in Visual
Representations and Interpretations, Ray Paton and Irene Nielson (Eds),
Springer-Verlag London 1999, 32-42. [translated into Lithuanian as `Matematika
ir mazgai', "alpha + omega", No.2 (6) (1998) 5-14.
pdf

102.
`Groupoids and crossed objects in
algebraic topology',
Homology,
homotopy and applications', 1 (1999) 1-78.
pdf (revised hyperref version)

103.
`Nusos, matematiques i art', Butll.
de la Soc. Catalana d. Matematiques, 13 (1998) 7-19. [Translated into Catalan
by Gemma Bastardas from an article `Knots, mathematics and art' published
in English in the Actes del VI Congres de Llenguatges Naturels i Llenguatges
Formals (Tarragona, 17-21 Sept, 1990).]

104. (with A. RAZAK SALLEH), ``Free crossed crossed resolutions
of groups and presentations of modules of identities among relations'' ,
London Math. Soc. J. Computation and Math. (2) (1999)
28-61.
pdf

105.
(with G.H. MOSA) `Double categories,
2-categories, thin structures and connections', Theory and Applications of
Categories, (1999), 163-175.

106.
`John Robinson's Symbolic Sculptures,
knots and mathematics', Proceedings ISAMA99, Ed N. Friedman and J. Barrallo,
University of the Basque Country (san Sebastian) 1999, 75-82.

107. (with A. Heyworth) `Using rewriting systems to compute left
Kan extensions and induced actions of categories', J. Symbolic Computation
29 (2000) 5-31.
pdf

108. `Dismay and decadence in British Universities', letter to —
Science & Public Affairs, August, 1999, p. 28.

109.
`Mathematical themes in the sculptures
of John Robinson : 1 Borromean sculptures' Mathematics Today 36 (1)
(2000) 6-7.

110.
Review of `History of Topology' ed
I M James, — London Math Soc. Newsletter, Jan 2000, 25-27. pdf

111.
(with T. Porter) `Mathematical Structure:
Knowledge, Representation and Interpretation', in Theoria et Historia
Scientiarum, the International Journal of Interdisciplinary Studies, special
issue on `Knowledge: representations and interpretations', edited W. Meyer
and R. Paton. 6 (2002) 39-54.

112.
`The symbolic sculptures of John
Robinson', in Theoria et Historia
Scientiarum, the International Journal of Interdisciplinary Studies, issue
on `Knowledge: representation and interpretation.', edited W. Meyer and R.
Paton, 6 (2002) 55-73.

113.
(with İ. İÇEN ), 'Locally Lie
subgroupoids and their Lie holonomy and monodromy groupoids', \it Top. and
its Appl. 115 (2000) 125-138.
pdf

113a.`Mathematical themes in the sculptures of John Robinson : 2
Polyhedra' Mathematics Today 36 (6) (2000) 172-173.

114.
(with M. GOLASINSKI, T.PORTER and A.P.TONKS), ``Spaces of maps into classifying
spaces for equivariant crossed complexes, II: The general topological group
case.'' K-theory 23 (2001) 129-155.
pdf

115. (with İ. İÇEN ), `Homotopies and automorphisms of crossed modules
of groupoids', Applied Categorical Structures, 11

(2003) 185-206.
pdf

116. (with F. A. Al-Agl and R. STEINER), ``Multiple categories:
the equivalence of a globular and a cubical approach'', Advances in Mathematics
170 (2002) 71-118.
pdf

117.
(with T. PORTER),
``The methodology
of mathematics'', European Mathematical
Society Newsletter June (2001) 12-14, Sept. (2001) 14-16.

118.(with K.HARDIE, H.KAMPS, T. PORTER), `` The homotopy double
groupoid of a Hausdorff space'',
Theory and Applications of Categories, 10 (2002)
71-93.

119. (with İ. İÇEN and O. MUCUK) `Holonomy and monodromy groupoids',
in Lie Algebroids, Banach Center Publications Institute of Mathematics, Polish
Academy of Sciences, Warsaw, 54 (2001) 9-20.
pdf

120.
`Algebraic homotopy', Supplement III
Encyclopaedia of Mathematics Managing Editor: M. Hazewinkel Kluwer Academic
Publishers (2002) 29-31.

121.
`Exponential law in topology', Supplement
III Encyclopaedia of Mathematics Managing Editor: M. Hazewinkel Kluwer Academic
Publishers (2002) 142-143.

122.
(with İ. İÇEN, and O. MUCUK),
`Examples and coherence properties of local subgroupoids', Topology and its
Applications 127 (2003) 393-408.

123. (with İ. İÇEN) `Towards a 2-dimensional notion of holonomy',
Advances in Math. 178 (2003) 141-175.
pdf

124. (with C.D.WENSLEY), `Computation and homotopical applications
of induced crossed modules', J. Symbolic Computation 35 (2003) 59-72.
pdf

125.
(with M. BULLEJOS and T.PORTER), `Crossed
complexes, free crossed resolutions and graph products of groups', Proceedings
Workshop Korea 2000, Heldermann Verlag. 27 (2003) 11-26.
pdf

126. (with E. MOORE, T.PORTER, C.D.WENSLEY), `Crossed complexes,
and free crossed resolutions for amalgamated sums and HNN-extensions of groups',
UWB Math Preprint 02-09. math.AT/0207037 Georgian Math. J. 9 (2002) 623-644.
pdf

127.
`Serie di sculture simboliche
dell'universo di John Robinson', in — Matematica, arte, tecnologia, cinema,
edited Michele Emmer, Mirella Manaresi, Springer-Verlag Italia, Milano, 2002,
19-30.

128.
`Forum discussion', in Mathematics
and Art,: Mathematical Visualisation in Art and Education, Editor Claude
P . Bruter, Springer-Verlag (Berlin Heidelberg) 2002, 155-159.

129. (with G. JANELIDZE), `Galois Theory and a new homotopy double
groupoid of a map of spaces', Applied Categorical Structures 12 (2004) 63-80.
pdf

130. (with T. PORTER), `The intuitions of higher dimensional algebra
for the study of structured space', Revue de Synthèse, 124 (2003)
173-203. ` UWB Math. Preprint (pdf
file).

131. (with HIGGINS, P.J.), `Cubical abelian groups with connections
are equivalent to chain complexes',
Homology, Homotopy and
Applications, 5(1) (2003) 49-52.

132. `Crossed complexes and homotopy groupoids as non commutative
tools for higher dimensional local-to-global problems', Proceedings of the
Fields Institute Workshop on Categorical Structures for Descent and Galois
Theory, Hopf Algebras and Semiabelian Categories, September 23-28, 2002,
Fields Institute Communications 43 (2004)
101-130. pdf of revised
version

133. `Les escultures simbóliques de John Robinson', Métode,
Universitat de Valencia, Revista de Difusiò de la Investigaciò, Primavera
2003, no. 37, 67-71.

134. (with J.F. Glazebrook), `Connections, local subgroupoids, and
a holonomy Lie groupoid of a line bundle gerbe', Univ. Iagel. Acta Math.
XLI (2003) 283-296 (UWB Math Preprint
02.22).

135. (with H.B. Griffiths) `Obituary: W.H. Cockcroft', Bull. London
Math. Soc. 37 (2005) 149-155.

136. (with T. Porter), `Category theory and higher dimensional
algebra: potential descriptive tools in neuroscience', Proceedings of the
International Conference on Theoretical Neurobiology, Delhi, February 2003,
edited by Nandini Singh, National Brain Research Centre, Conference Proceedings
1 (2003) 80-92. pdf

137. (with R.Paton and T. Porter), `Categorical language and
hierarchical models for cell systems', Computation in Cells and Tissues -
Perspectives and Tools of Thought, Paton, R.; Bolouri, H.; Holcombe, M.;
Parish, J.H.; Tateson, R. (Eds.) Natural Computing Series, Springer (2004)
289-303. pdf

138. `𝒌-spaces', in Encyclopedia of General Topology, ed. K.P.Hart,
J. Nagata, and J.E. Vaughan, Elsevier (2004) 189-191.
pdf

139.
(with N. Ghani, A.Heyworth, C.D.Wensley),
`String rewriting systems for double coset systems', J. Symb. Comp. 41 (2006)
573-590.UWB Math Preprint 04.04.
arXiv:math/0508391

140. (with H. Kamps and T. Porter), `A homotopy double groupoid
of a Hausdorff space II: a van Kampen theorem',
Theory and Appl.
Cat.14, (2005) 200-220.

141. `John Robinson's Symbolic Sculptures: Knots and mathematics',
in `The visual mind II', edited Michele Emmer, MIT Press, (2005) 125-139.

142.
`Mathematicians struggle for truth',
Letter to the Independent, Aug
17, 2005.

143. `Allow beautiful minds to thrive', letter in the Times
HigherEducational Supplement, September 16, 2005.

144. `Origins of Grothendieck's Pursuing Stacks', Letter, Notices
American Math. Soc., 52 (8) Sept, 2005, 830.

145. (with I. C. Baianu, G.
Georgescu, and J. F. Glazebrook), `Complex nonlinear biodynamics in categories:
higher dimensional algebra, and Lukasiewicz--Moisil Topos: transformations
of neuronal, genetic and neoplastic networks', Axiomathes 16 (2006)
65-122.

146.
(with T. Porter) `Category Theory:
an abstract setting for analogy and comparison', In: What is Category Theory?
Advanced Studies in Mathematics and Logic, Polimetrica Publisher, Italy,
(2006) 257-274.
pdf

147. `Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids;
Higher dimensions', Proceedings of the 7th Conference on the Geometry and
Topology of Manifolds: The Mathematical Legacy of Charles
Ehresmann, Bedlewo (Poland) 8.05.2005-15.05.2005, Banach Centre
Publications 76, Institute of Mathematics Polish Academy of Sciences, Warsaw,
(2007) 51-63. (math.DG/0602499).
pdf

148. (with Bak, A., Minian, G., and Porter, T.), `Groupoid atlases:
an Introduction', abstract of talk to the `Colloque International: Charles
Ehresmann: 100 ans', Amiens 7-9 October, 2005, Cah. Top. Géom. Diff. Cat.
46 (2005) 183.

149.
(with Bak, A., Minian, G., and Porter,
T.), `Global actions, groupoid atlases and applications',
J. Homotopy
and Related Structures, 1 (2006) 101-167.
pdf

150. (with T. Porter), `Analogy, concepts and methodology in
mathematics', Eureka, (September 2006) 23-27. UWB Math Preprint 06.08.
pdf

151. `Groupoids, the Phragmen-Brouwer property and the Jordan curve
theorem', J. Homotopy and Related Structures 1 (2006) 175-183.
arXiv:math/0607229
pdf

152. (with R. Sivera), `Normalisation for the fundamental crossed complex
of a simplicial set', J. Homotopy and Related Structures, Special
Issue devoted to the memory of Saunders Mac Lane, 2 (2007) 49-79.
math.AT/0611728
.
pdf

153. `Promoting Mathematics', MSOR Connections 7 no 2 July 2007 21-25.
pdf

154. `John Robinson Sculptor, May 5 1935-April 6, 2007',
Hyperseeing, June 2007, 3-7.
pdf

155. `John Robinson, The Sculptor', LMS Newsletter, July 2007, p.8.
pdf

156. (with I. C. Baianu and J. F.
Glazebrook), ` Categorical Ontology of Complex Space-Time Structures: The
Emergence of Life and Human Consciousness', Axiomathes,
**17:**
(2007) 223-352.
pdf

157. (with I. C. Baianu and J. F.
Glazebrook), `A Conceptual Construction for Complexity Levels Theory in SpaceTime
Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics
and Dynamic Systems', Axiomathes , **17 **(2007) .
pdf

158. (with I. C. Baianu and J. F. Glazebrook), `A Non--Abelian Categorical
Ontology and Higher Dimensional Algebra of Spacetimes and Quantum Gravity'.
Axiomathes , **17 **(2007)
353-408
pdf

159 (with I. C. Baianu and J. F. Glazebrook), CATEGORICAL ONTOLOGY
OF COMPLEX SYSTEMS, META--SYSTEMS AND LEVELS: The Emergence of life, Human
Consciousness and
Society'. In: ``Theory and Applications
of Ontology." vol.1, R. Poli, et al., eds. 2008, Springer: Berlin (in
press).

160. `Remembering
George Mackey',
Letter, Notices American Mathematical
Society, 54 no.10 , November, 2007,
p.1280.

161. `Mathoetic mode', Newsletter, London Mathematical Society, January 2008,
p.26. html

162. `A new higher homotopy groupoid: the fundamental globular omega-groupoid
of a filtered space', Homotopy, homology and applications, 10 (2008), No.
1, pp.327-343. pdf

163. with I. Morris, J. Shrimpton and C.D. Wensley, `Graphs of Morphisms
of Graphs', Electronic
Journal of Combinatorics, A1 of Volume 15(1), 2008. 1-28.
pdf

164. `Exact sequences of fibrations of crossed complexes, homotopy classification
of maps, and nonabelian extensions of groups', J. Homotopy and Related Structures
3 (2008) 331-343. pdf

165. `Crossed complexes and homotopy groupoids as non commutative tools for
higher dimensional local-to-global problems', in Michiel Hazewinkel (ed.),
Handbook of Algebra, volume 6, Elsevier, 2009, p. 83-124. (revised version
of [132] available as math.AT/0212274 v7).
pdf

166. `Memory evolutive systems', Axiomathes, 19 (2009) 271-280. (Review
of book by A-C. Ehresmann and J.P. Vanbremeersch).
pdf

167. I.C. Baianu, J.F. Glazebrook and R. Brown, `Algebraic topology foundations
of supersymmetry and symmetry breaking in quantum field theory and quantum
gravity: a review' SIGMA (Symmetry, Integrability, and Geometry: Methods
and Applications) 79 pp. pdf

168. R. Brown and R. Sivera, `Algebraic colimit calculations in homotopy
theory using fibred and cofibred categories', Theory and Applications
of Categories, 22 (2009) 222-251 . pdf

169. `Promoting mathematics', EMS Newsletter, June 2010, 17-21.
pdf
of whole issue
pdf of article

170. `Possible connections between whiskered categories and groupoids, Leibniz
algebras, automorphism structures and local-to-global questions', J. Homotopy
and Related Structures, 5(1) (2010)
305-318. pdf

171. R. Brown and R. Street, `Covering morphisms of crossed complexes and
of cubical ω-groupoids are closed under tensor product', Cah. Top. Geom.
Diff. Cat., 52 (2011) 188-208. pdf

172. `Erratum to ``Possible connections between whiskered categories and groupoids, Leibniz algebras,
automorphism structures and local-to-global questions ",
vol.5 (1) 2010, pp.305-318.' J. Homotopy and Related Structures (2011) (to appear). pdf

173. with I. Baianu and J. Glazebrook, ``Quantum Symmetries, Operator Algebra and Quantum Groupoid Representations: Paracrystalline Systems, Topological Order, Supersymmetry and Global Symmetry Breaking",
International Journal of Research and Reviews in Applied Sciences, 9, Issue 2 (November, 2011) 163--206. pdf

174. with T. Porter, ``What should be the *context* of an adequate specialist undergraduate education in mathematics?'', The De Morgan Journal 2 no. 1, (2012) 411--67.
pdf

175. with J. Glazebrook, ``A Career of Unyielding Exploration: In Memory of
Ion C. Baianu (1947–2013)", Quanta, (2) No 1 (2013) 1--6.
html pdf

176. with O. Antolin Camarena, ``Corrigendum to ``Groupoids, the Phragmen-Brouwer Property, and the Jordan
Curve Theorem'', J. Homotopy and Related Structures 1 (2006) 175-183.'' J. Homotopy and Related Structures (to appear)
4pp pdf

177. "Modelling and Computing Homotopy Types: I", Indagationes Math. (special issue in honor of L.E.J. Brouwer to appear in 2017).
pdf Online final

178. "Tutorials for mathematics students", The De Morgan Gazette 9
no.~2 (2017), 7–10. bit.ly/2lGUhj2 Journal copy

179. with T. Porter, The methodology of mathematics, The De Morgan Gazette 9 no. 5 (2017), 27–38. bit.ly/2xH4kOy
Journal pdf

Rough Analysis of types of output

Papers on teaching: 10a, 56, 67, 80, 81, 87, 90, 99, 100, 153, 169, 174.

Papers on Popularisation: 63, 64, 65, 77, 79, 83, 101, 103, 106, 108, 117, 127, 128, 133, 161.

General expositions: 58, 78, 111, 112, 135, 136

Research Papers: The rest.

Papers in preparation

P2. (with C.D.WENSLEY), ``On sorting sequences''.
02.25 BROWN,
R. & HIGGINS, P.J.

The fundamental groupoid of the quotient of a Hausdorff space by a discontinuous
action of a discrete group is the orbit groupoid

Preprints not yet published

82.2 ``Holonomy and monodromy groupoids'', U.C.N.W.
Pure Math. Preprint 82.2, 10pp.

86.4 ``A convenient category of topological spaces: historical note'', U.C.N.W.
Pure Math. Preprint 86.4, 3pp.

88.11 (with G.H.MOSA), ``Double categories, $R$-categories, and crossed
modules'', U.C.N.W. Mathematics Preprint 88.11, 13pp.

89.12 (with N.D. GILBERT and J. SHRIMPTON), ``Symmetry objects in closed
categories'', 24pp.

90.23 ``The sculptures of John Robinson'', 9pp.

91.14 (with N.D.GILBERT, H.-J.HOEHNKE and J.SHRIMPTON), ``Non-Abelian tensor
products of groups; groupoids; quadratic forms; and higher order symmetry'',
53pp, UCNW Math Preprint 91.14.

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