Homology of Coxeter and Artin groups

Introduction to Coxeter and Artin groups......Page 5
Results: Low dimensional homology of Coxeter groups......Page 7
Results: Homological stability for Artin Monoids......Page 13
1.1. Definition and examples......Page 18
1.2. Products and subgroups......Page 21
1.3. The Davis complex......Page 24
2.1. Discussion of results......Page 29
2.2. Outline of proof......Page 37
2.3. Introduction to the isotropy spectral sequence......Page 38
2.4. Calculation for H2(W;Z)......Page 49
2.5. Calculation for H3(W;Z)......Page 56
3.1. Definition and examples......Page 99
3.2. The K(,1) conjecture......Page 101
4.2. Divisors in Artin monoids: general theory......Page 105
4.3. Divisors in Artin monoids: theory for proof......Page 107
4.5. Semi-simplicial constructions with monoids......Page 110
5.1. Definition and examples......Page 119
5.2. Homological stability for Coxeter groups......Page 120
5.3. Homological stability for Artin groups: literature review......Page 121
6.1. Discussion of results......Page 123
6.3. Preliminaries concerning the sequence of Artin monoids......Page 125
6.4. The semi-simplicial space An......Page 126
6.5. High connectivity......Page 131
6.6. Proof of Theorem C......Page 148
A.1. Code......Page 155
Examples......Page 156
Appendix B. Calculations for Section 2.5......Page 159
Bibliography......Page 194