Philip J Higgins

[RONALD BROWN <ronnie.profbrown@btinternet.com>]

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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