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E-raamat: Geometry and Topology of Coxeter Groups

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Geometry and Topology of Coxeter GroupsSuurem pilt
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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 Hopfs theory of ends, contractible manifolds and homology spheres, the Poincaré Conjecture, and Gromovs 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.
Chapter
1. Introduction and preview.
Chapter
2. Some basic notions in
geometric group theory.
Chapter
3. Coxeter groups.
Chapter
4. More
combinatorics of Coxeter groups.
Chapter
5. The basic construction.
Chapter
6. Geometric reflection groups.
Chapter
7. The complex E.
Chapter
8. The
algebraic topology of U and of E.
Chapter
9. The fundamental group and the
fundamental group at infinity.
Chapter
10. Actions on manifolds.
Chapter
11. The reflection group trick.
Chapter
12. E is CAT(0).
Chapter
13.
Rigidity.
Chapter
14. Free quotients and surface subgroups.
Chapter
15.
Another look at (co)homology.
Chapter
16. The Euler characteristic.
Chapter
17. Growth series.
Chapter
18. Artin Groups.
Chapter
19. L2-Betti numbers
of Artin groups.
Chapter
20. Buildings.
Chapter
21. Hecke - von Neumann
algebras.
Chapter
22. Weighted L2- (co)homology.
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.
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