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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Hopf ring structure on the mod $p$ cohomology of symmetric groups

Lorenzo Guerra

Algebraic & Geometric Topology 17 (2017) 957–982
Abstract

We describe a Hopf ring structure on n0H(Σn; p), discovered by Strickland and Turner, where Σn is the symmetric group of n objects and p is an odd prime. We also describe an additive basis on which the cup product is explicitly determined, compute the restriction to modular invariants and determine the action of the Steenrod algebra on our Hopf ring generators. For p = 2 this was achieved in work of Giusti, Salvatore and Sinha, of which this work is an extension.

Keywords
group cohomology, symmetric group, Hopf ring, Dyer–Lashof operations, Steenrod algebra, Mui invariants
Mathematical Subject Classification 2010
Primary: 20J06
References
Publication
Received: 9 November 2015
Revised: 16 September 2016
Accepted: 30 September 2016
Published: 14 March 2017
Authors
Lorenzo Guerra
Scuola Normale Superiore
Piazza dei Cavalieri 7
I-56126 Pisa
Italy