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Roger C Lyndon

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18 Dec 1917

Calais, Maine, USA

8 June 1988

Roger Lyndon's mother died when he was two years old and his family moved to various towns so, as a consequence, his education took place at a number of different schools. He graduated from Derby School in 1935 and entered Harvard University with the aim of studying literature so that he might become a writer. However, he discovered that, for him, mathematics was easy and required little effort while he had to spend long hours learning literature. The move to mathematics was made and he graduated from Harvard in 1935.

Having worked for a year in a bank in Albuquerque, Lyndon returned to Harvard, being awarded a Master's Degree in 1941. He taught at Georgia Tech in session 1941/42, then he returned to Harvard for the third time in 1942 and there taught navigation to pilots while he studied for his doctorate. He was awarded a Ph.D. in 1946 for a thesis on homological algebra , the work being an outstanding early step in the study of spectral sequences. His supervisor was Saunders Mac Lane and his thesis was entitled The Cohomology Theory of Group Extensions.

After attending a course by Tarski , Lyndon and Tarski became good friends and Lyndon was later to work on model theory as a result of attending these lectures. Accepting a position at Princeton, he attended a course on knot theory by R Fox and from this his interest was aroused in combinatorial group theory. Reidemeister was at Princeton for a year in 1948 and again this was a major influence on Lyndon to work on group presentations .

Lyndon's first work which came out of these discussions with Reidemeister was published in 1950. In it Lyndon investigated one-relator groups. In particular he computed their cohomology groups.

In 1953 Lyndon left Princeton to take up a professorship at the University of Michigan where he remained throughout his career except for a number of posts as visiting professor at Berkeley, Queen Mary College, London, Montpellier, France and Picardie, France.

K I Appel, writes in :

Lyndon produces elegant mathematics and thinks in terms of broad and deep ideas.... I once asked him whether there was a common thread to the diverse work in so many different fields of mathematics, he replied that he felt the problems on which he had worked had all been combinatorial in nature... on would certainly have to put him in the very first rank of those who have used combinatorial techniques in the last forty years.

Lyndon made numerous major contributions to combinatorial group theory. These include the development of 'small cancellation theory', work on Fuchsian groups and the Riemann - Hurwitz formula, his introduction of 'aspherical' presentations of groups and his work on length functions in free products of groups.

Lyndon was the coauthor of one of the most important works on combinatorial group theory. Together with Paul Schupp, he wrote Combinatorial group theory (1976). I [EFR] remember how eagerly the book was awaited by those interested in research in this area, and the excitement of seeing the book when it first appeared and was passed round a lecture theatre at a conference I was attending.

Source:School of Mathematics and Statistics University of St Andrews, Scotland