#### Volume 18, issue 1 (2018)

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Second mod $2$ homology of Artin groups

### Toshiyuki Akita and Ye Liu

Algebraic & Geometric Topology 18 (2018) 547–568
##### Abstract

In this paper, we compute the second mod $2$ homology of an arbitrary Artin group, without assuming the $K\left(\pi ,1\right)$ conjecture. The key ingredients are (A) Hopf’s formula for the second integral homology of a group and (B) Howlett’s result on the second integral homology of Coxeter groups.

##### Keywords
Artin groups, Coxeter groups, group cohomology
##### Mathematical Subject Classification 2010
Primary: 20F36, 20J06
Secondary: 20F55
##### Publication
Received: 19 February 2017
Revised: 28 June 2017
Accepted: 16 July 2017
Published: 10 January 2018
##### Authors
 Toshiyuki Akita Department of Mathematics Hokkaido University Sapporo 060-0810 Japan Ye Liu Department of Mathematics Hokkaido University Sapporo Japan