The low-dimensional homology of finite-rank Coxeter groups

Boyd, Rachael

doi:10.2140/agt.2020.20.2609

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The low-dimensional homology of finite-rank Coxeter groups

Rachael Boyd

Algebraic & Geometric Topology 20 (2020) 2609–2655

DOI: 10.2140/agt.2020.20.2609

Abstract

We give formulas for the second and third integral homology of an arbitrary finitely generated Coxeter group, solely in terms of the corresponding Coxeter diagram. The first of these calculations refines a theorem of Howlett, while the second is entirely new and is the first explicit formula for the third homology of an arbitrary Coxeter group.

Keywords

Coxeter groups, group homology

Mathematical Subject Classification 2010

Primary: 20F55, 20J05, 20J06, 55T05

References

Publication

Received: 23 April 2019

Revised: 6 January 2020

Accepted: 20 January 2020

Published: 4 November 2020

Authors

Rachael Boyd
Max Planck Institute for Mathematics Bonn Germany

Volume 20, issue 5 (2020)