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The Geometry and Topology of Coxeter Groups

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 Character...

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Главный автор: Davis, Michael W. (Автор)
Соавтор: SpringerLink (Online service)
Формат: Электронный ресурс eКнига
Язык:английский
Опубликовано: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Редактирование:2nd ed. 2025.
Серии:Springer Monographs in Mathematics,
Предметы:
Group theory.
Manifolds (Mathematics).
Group Theory and Generalizations.
Manifolds and Cell Complexes.
Online-ссылка:https://doi.org/10.1007/978-3-031-91303-7
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Оглавление:
  • 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.

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