The low-dimensional homology of finite-rank Coxeter groups

DOI10.2140/AGT.2020.20.2609arXiv1811.00400MaRDI QIDQ6309083

Publication date: 1 November 2018

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.

Mathematics Subject Classification ID

Cohomology of groups (20J06) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Homological methods in group theory (20J05) General theory of spectral sequences in algebraic topology (55T05)

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