Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

Equivariant Steinberg summands

Pages: 203 – 220

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a13


Krishanu Sankar (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)


We construct Steinberg summands of $G$-equivariant spectra with $\operatorname{GL}_n (\mathbb{F}_p)$-action. We prove a lemma about their fixed points when $G$ is a $p$-group, and then use this lemma to compute the fixed points of the Steinberg summand of the equivariant classifying space of $(\mathbb{Z} / p)^n$. These results will be used in a companion paper to study the layers in the $\operatorname{mod}$ $p$ symmetric power filtration for $H \underline{\mathbb{F}}_p$.


equivariant, homology, homotopy

2010 Mathematics Subject Classification

20C20, 20G40, 55P42, 55P91

Copyright © 2020, Krishanu Sankar. Permission to copy for private use granted.

Received 27 May 2019

Accepted 5 November 2019

Published 29 April 2020