Representation-graded Bredon homology of elementary abelian 2-groups

Hausmann, Markus; Schwede, Stefan

doi:10.2140/agt.2025.25.4321

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Representation-graded Bredon homology of elementary abelian $2$-groups

Markus Hausmann and Stefan Schwede

Algebraic & Geometric Topology 25 (2025) 4321–4340

DOI: 10.2140/agt.2025.25.4321

Abstract

We calculate the representation-graded Bredon homology rings of all elementary abelian $2$ -groups with coefficients in the constant mod- $2$ Mackey functor. We exhibit minimal presentations for these rings as quotients of the polynomial algebra on the pre-Euler and inverse Thom classes of all nontrivial characters, subject to an explicit finite list of relations arising from orientability properties. Two corollaries of our presentation are the calculation, originally due to Holler and Kriz, of the geometric fixed point rings, and a strengthening of a calculation of Balmer and Gallauer of the localized twisted cohomology ring.

Keywords

Bredon homology, elementary abelian $2$-groups

Mathematical Subject Classification

Primary: 55N91, 55P91, 55Q91

References

Publication

Received: 20 April 2024

Accepted: 14 September 2024

Published: 29 October 2025

Authors

Markus Hausmann
Mathematisches Institut Universität Bonn Bonn Germany

Stefan Schwede
Mathematisches Institut Universität Bonn Bonn Germany

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

Volume 25, issue 7 (2025)