George W. Mackey

In reponse to the reports on George W. Mackey in the Notices [July, 2007], I would like to say how he decisely influenced my research for four decades.

In April, 1967, I gave an invited talk to the British Mathematical Colloquium (Swansea) on a new groupoid version of the traditional van Kampen theorem for the fundamental group of a pointed space. At tea time, I was told: `That was very interesting. I have been using groupoids for years. My name is Mackey.'

He then told me of his work on groupoids and ergodic theory. It occurred to me that if people from two or three different areas found the idea of groupoid significant, then there was probably much more in this than I had previously thought.

An immediate effect was for me to add a chapter on covering spaces to the book on topology which I was writing, since Mackey used strongly the action groupoid of a group action.

When I came to Bangor in 1970, I set students to work on topological groupoids (Lew Hardy) and measured groupoids (Tony Seda). Eventually, Tony's thesis was on Haar measure for groupoids, and later Mackey told me he also had a student working on this!

The replacement of groups by groupoids allowed for higher homotopy groupoids, and their applications, as structures in some sense `more non commutative' than groups (or groupoids).

It was only in 1981 that I learned from Jean Pradines, and began to understand, Charles Ehresmann's extensive work on Lie groupoids, and their applications to local-to-global problems.

Though we met only a few further times, Mackey's conceptual approach to mathematics was an encouraging example in all this. He made his own evaluations of potential importance. In his field, he followed Dirac's dictum:: `You should follow a mathematical idea wherever it leads ..." and was undistracted from this by what is called `the mainstream'. He was truly a professional.

Ronnie Brown
Emeritus Professor
University of Wales, Bangor
www.bangor.ac.uk/r.brown

(Submitted July 12, 2007)