RE: Philip J Higgins

["Linton, Fred" <flinton@wesleyan.edu>]

One by one, alas, we are slowly being whittled away. I mourn this loss.

-- Fred Linton
________________________________________
From: RONALD BROWN [ronnie.profbrown@btinternet.com]
Sent: Wednesday, April 22, 2015 05:59
To: categories@mta.ca
Subject: categories: Philip J Higgins

I heard yesterday, April 21, that Philip Higgins died on 25 March,
peacefully in an armchair, from heart conditions.

His 1964 paper on "Presentations of groupoids with applications to groups"
introduced me to the idea that groupoids could be used for algebraic
computations. A key construction in this paper is that of a new groupoid
U_f(G) over Y from a groupoid G and a function f: Ob(G)  --> Y. This
construction easily gives free groups and free products of groups, and has
important higher dimensional generalisations. This paper led me to a
Seifert-van Kampen theorem for the fundamental grouoid on a set of base
points, allowing applications to unions of spaces for which they or their
intersections are not connected, such as the circle.

This work led in 1974 to a long term collaboration
on higher groupoids and their applications.

He had a wonderful way of organising complex algebraic material, and much
of this expository skill is shown in the book

R. Brown, P.J. Higgins, R. Sivera,   "Nonabelian algebraic
topology: filtered spaces, crossed complexes, cubical homotopy
groupoids", EMS Tracts in Mathematics Vol. 15, 703 pages. (August
2011).

where major central parts are lifted from our joint papers.  When he got
into a new subject, he saw ways of clarifying the matter and exposition.
This is shown in his work with Kirill Mackenzie on Lie groupoids and
algebroids. His early work on groups with operators, and on the algebraic
theory of algebras with partial operations, are still refereed to.

At one time he had to choose between two professions, and decided he could
have more fun as a professional mathematician and an amateur violinist.

His craftmanship is shown that in his retirement he took up again making
for his grandchildren violins, violas and cellos, each one taking about a
year. I miss a good friend.

Ronnie Brown



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