We describe a Hopf ring structure on ⊕n>0 H*(Σn; Zp), 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 D 2 this was achieved in work of Giusti, Salvatore and Sinha, of which this work is an extension.

Hopf ring structure on the mod p cohomology of symmetric groups

GUERRA, LORENZO
2017

Abstract

We describe a Hopf ring structure on ⊕n>0 H*(Σn; Zp), 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 D 2 this was achieved in work of Giusti, Salvatore and Sinha, of which this work is an extension.
2017
Settore MAT/07 - Fisica Matematica
Dyer–Lashof operations; Group cohomology; Mui invariants; Steenrod algebra; Symmetric group; Geometry and Topology
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79094
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