Geodesic
Hopf ring structure on the mod p cohomology of symmetric groups
Guerra, Lorenzo1
1Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 957-982
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We describe a Hopf ring structure on ⊕ n≥0H∗(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 = 2 this was achieved in work of Giusti, Salvatore and Sinha, of which this work is an extension.

DOI : 10.2140/agt.2017.17.957
Classification : 20J06
Keywords: group cohomology, symmetric group, Hopf ring, Dyer–Lashof operations, Steenrod algebra, Mui invariants

Guerra, Lorenzo  1

1 Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy 
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Guerra, Lorenzo. Hopf ring structure on the mod p cohomology of symmetric groups. Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 957-982. doi: 10.2140/agt.2017.17.957

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