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

In this paper, we compute the second mod 2 homology of an arbitrary Artin group, without assuming the K(π,1) 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.

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