Volume 20, issue 5 (2020)

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The low-dimensional homology of finite-rank Coxeter groups

Rachael Boyd

Algebraic & Geometric Topology 20 (2020) 2609–2655

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.

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Coxeter groups, group homology
Mathematical Subject Classification 2010
Primary: 20F55, 20J05, 20J06, 55T05
Received: 23 April 2019
Revised: 6 January 2020
Accepted: 20 January 2020
Published: 4 November 2020
Rachael Boyd
Max Planck Institute for Mathematics