Dyer-Lashof operations on Tate cohomology of finite groups.
type: Item
instance of: scholarly article
title: Dyer-Lashof operations on Tate cohomology of finite groups.
zbMATH Open document ID: 1278.20071
author: Martin Langer
published in: Algebraic \& Geometric Topology
publication date: 2012-05-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1003.5595
review text: Let \(p\) be a prime number, \(G\) be a finite group and \(\widehat{H^*}(G,\mathbb F_p)\) be the Tate cohomology of \(G\). In this paper, the author constructs power operations of Dyer-Lashof type on \(\widehat{H^*}(G,\mathbb F_p)\) by exhibiting an \(E_\infty\)-operad action on \(\Hom(\mathcal P,\mathbb F_p)\) for a complete projective resolution \(\mathcal P\) of the trivial \(\mathbb F_p[G]\)-module \(\mathbb F_p\). He gives some properties and applications of these operations. In particular, he shows that they agree with the Steenrod operations on \(H^*(G,\mathbb F_p)\).
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 55S12
zbMATH DE Number: 6035495
zbMATH Keywords: Tate cohomology
zbMATH Keywords: Dyer-Lashof operations
zbMATH Keywords: cohomology operations
zbMATH Keywords: finite groups
zbMATH Keywords: Steenrod operations
reviewed by: Saïd Zarati
MaRDI profile type: Publication
OpenAlex ID: W3101937618
arXiv ID: 1003.5595
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DOI: 10.2140/AGT.2012.12.829
description: scientific article; zbMATH DE number 6035495