Groups: Topological, Combinatorial and Arithmetic Aspects
This book contains the proceedings of a meeting held in 1999 in Bielefeld. The subject of the meeting was quite broad, covering many different aspects of infinite (and finite) groups. There are altogether 17 contributions, comprising both review and research papers. A long survey written by I. M. Chiswell (150 pages) describes the theory of Euler characteristics, covering its various definitions and relations. Short reviews of basic homology algebra and the cohomological dimension of a group are included. The paper by J. R. Parker and C. Series is devoted to the mapping class group of a torus with punctures. It first describes a simpler case of the torus with one puncture. Generalizing this case step by step, the authors describe the mapping class group of the torus with two punctures. Three papers by A. Mann (applications of probability in group theory), T. W. Müller (parity pattern in Hecke groups and Fermat primes) and D. Segal (finite images of infinite groups) are devoted to various aspects of the theory of subgroup growth. The contribution by B. Remy (based on his PhD thesis) treats the Kac-Moody groups from a combinatorial point of view. The paper by E. B. Vinberg and R. Kaplinsky is devoted to pseudo-finite generalized triangle groups. There are ten other shorter contributions in the book on various other topics, including topological properties of groups, the connections between groups and formal languages and automata, the Magnus-Nielsen method and hyperbolic lattices in dimension 3.