Chapter Twelve. Σ IS CAT(O): THEOREMS OF GROMOV AND MOUSSONG

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xiii
4. Chapter One. INTRODUCTION AND PREVIEW 1
5. Chapter Two. SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY 15
6. Chapter Three. COXETER GROUPS 26
7. Chapter Four. MORE COMBINATORIAL THEORY OF COXETER GROUPS 44
8. Chapter Five. THE BASIC CONSTRUCTION 63
9. Chapter Six. GEOMETRIC REFLECTION GROUPS 72
10. Chapter Seven. THE COMPLEX Σ 123
11. Chapter Eight. THE ALGEBRAIC TOPOLOGY OF U AND OF Σ 136
12. Chapter Nine. THE FUNDAMENTAL GROUP AND THE FUNDAMENTAL GROUP AT INFINITY 166
13. Chapter Ten. ACTIONS ON MANIFOLDS 176
14. Chapter Eleven. THE REFLECTION GROUP TRICK 212
15. Chapter Twelve. Σ IS CAT(O): THEOREMS OF GROMOV AND MOUSSONG 230
16. Chapter Thirteen. RIGIDITY 255
17. Chapter Fourteen. FREE QUOTIENTS AND SURFACE SUBGROUPS 276
18. Chapter Fifteen. ANOTHER LOOK AT (CO)HOMOLOGY 286
19. Chapter Sixteen. THE EULER CHARACTERISTIC 306
20. Chapter Seventeen. GROWTH SERIES 315
21. Chapter Eighteen. BUILDINGS 328
22. Chapter Nineteen. HECKE–VON NEUMANN ALGEBRAS 344
23. Chapter Twenty. WEIGHTED L2-(CO)HOMOLOGY 359
24. Appendix A: CELL COMPLEXES 401
25. Appendix B: REGULAR POLYTOPES 421
26. Appendix C: THE CLASSIFICATION OF SPHERICAL AND EUCLIDEAN COXETER GROUPS 433
27. Appendix D: THE GEOMETRIC REPRESENTATION 439
28. Appendix E: COMPLEXES OF GROUPS 449
29. Appendix F: HOMOLOGY AND COHOMOLOGY OF GROUPS 465
30. Appendix G: ALGEBRAIC TOPOLOGY AT INFINITY 477
31. Appendix H: THE NOVIKOV AND BOREL CONJECTURES 487
32. Appendix I: NONPOSITIVE CURVATURE 499
33. Appendix J: L2-(CO)HOMOLOGY 531
34. Bibliography 555
35. Index 573