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The mod $2$ cohomology of the infinite families of Coxeter groups of type $B$ and $D$ as almost-Hopf rings

Lorenzo Guerra

Algebraic & Geometric Topology 23 (2023) 3221–3292
Abstract

We describe a Hopf ring structure on the direct sum of the cohomology groups n0H(WBn; 𝔽2) of the Coxeter groups of type WBn, and an almost-Hopf ring structure on the direct sum of the cohomology groups n0H(WDn; 𝔽2) of the Coxeter groups of type WDn, with coefficients in the field with two elements 𝔽2. We give presentations with generators and relations, determine additive bases and compute the Steenrod algebra action. The generators are described both in terms of a geometric construction by De Concini and Salvetti and their restriction to elementary abelian 2–subgroups.

Keywords
Hopf ring, Coxeter groups, group cohomology, configuration spaces
Mathematical Subject Classification
Primary: 20F55, 20J06
Secondary: 20J05
References
Publication
Received: 7 September 2021
Revised: 30 April 2022
Accepted: 18 May 2022
Published: 26 September 2023
Authors
Lorenzo Guerra
Dipartimento di Matematica
Università di Roma Tor Vergata
Rome
Italy

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