Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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

Open Access made possible by participating institutions via Subscribe to Open.