The Geometry and Topology of Coxeter Groups
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Beschreibung
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.
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.
Provides a comprehensive study of Coxeter groups Introduces innovative constructions such as the Davis complex The second edition contains new chapters on Artin groups
Autor*in
Michael W. Davis
Themen in »The Geometry and Topology of Coxeter Groups«
Coxeter groups Buildings Reflection groups Cayley graphs CAT(0) groups Geometric group theory Artin groups Reflection group trick L2 Betti numbers Singer conjecture Borel conjecture Poincare conjecture
Stimmen zu »The Geometry and Topology of Coxeter Groups«
“This monograph offers a comprehensive and substantially expanded treatment of Coxeter groups and their applications to topology and geometry. ... the author has incorporated numerous refinements, corrections and new results that have emerged over the past fifteen years ... . This volume, complemented by J. E. Humphreys’ classic … remains a standard reference for researchers and advanced students interested in Coxeter groups, geometric group theory and their topological and geometric applications.” (Egle Bettio, zbMATH 1573.20001, 2026)
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