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Abstract
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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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Keywords
Coxeter groups, group homology
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Mathematical Subject Classification 2010
Primary: 20F55, 20J05, 20J06, 55T05
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Publication
Received: 23 April 2019
Revised: 6 January 2020
Accepted: 20 January 2020
Published: 4 November 2020
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