This book, now in a revised and extended second edition, offers an in-depth account of Coxeter groups through the perspective of geometric group theory. It examines the connections between Coxeter groups and major open problems in topology related to aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer Conjectures. The book also discusses key topics in geometric group theory and topology, including Hopf’s theory of ends, contractible manifolds and homology spheres, the Poincaré Conjecture, and Gromov’s theory of CAT(0) spaces and groups. In addition, this second edition includes new chapters on Artin groups and their Betti numbers. Written by a leading expert, the book is an authoritative reference on the subject.

Autorentext

Michael W. Davis received a PhD in mathematics from Princeton University in 1975. He was a Professor of Mathematics at Ohio State University for thirty-nine years, retiring in 2022 as Professor Emeritus. In 2015, he became a Fellow of the AMS. His research is in geometric group theory and topology. Since 1981, his work has focused on topics related to reflection groups including the construction of new examples of aspherical manifolds and the study of their properties.