Second mod 2 homology of Artin groups

Akita, Toshiyuki; Liu, Ye

doi:10.2140/agt.2018.18.547

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Second mod $2$ homology of Artin groups

Toshiyuki Akita and Ye Liu

Algebraic & Geometric Topology 18 (2018) 547–568

DOI: 10.2140/agt.2018.18.547

Abstract

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.

Keywords

Artin groups, Coxeter groups, group cohomology

Mathematical Subject Classification 2010

Primary: 20F36, 20J06

Secondary: 20F55

References

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

Volume 18, issue 1 (2018)