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Modular coinvariants and the mod p homology of QS^k

Le : 24/02/2016 14h00
Par : Phan Hoàng Chơn (Saigon)
Lieu : I 103
Lien web :
Résumé : It is well-known that, as a ring object in the category of coalgebras (also known as a coalgebraic ring or a Hopf ring) the mod p homology of QS^k_{k>=0} is generated by the image of the mod p homology of B\Sigma _p and S^1. In this talk, we use modular invariant theory to establish a complete set of relations for odd prime p, the case p=2 having been previously treated by Paul Turner. We also describe the action of the mod p Dyer–Lashof algebra as well as the mod p Steenrod algebra on the coalgebraic ring. One can derive the mod p homology of the \Sigma _n's as well as the maps induced in mod p homology by \Sigma _n\times \Sigma _m --> \Sigma _{n+m} and \Sigma _n\times \Sigma _m ---> \Sigma _{nm}.