Cohomology Of Symmetric Groups Research Articles

Correction to the article Hopf ring structure on the mod p cohomology of symmetric groups

Correction to the article Hopf ring structure on the mod p cohomology of symmetric groups

The cohomology of symmetric groups and the Quillen map at odd primes

Gunawardena, Lannes, and Zarati proved that the Quillen homomorphism q G : H ∗BG→ lim ← C(G) H ∗BE is an isomorphism for G= Σ n at p=2, but fails to be an isomorphism for odd primes. We prove that at odd primes, the restriction of the Quillen map to the subring of elements that are annihilated by all Steenrod operations that involve the Bockstein is an isomorphism for all n.

Homotopy operations for simplicial commutative algebras

The indicated operation algebra is studied by methods dual to the usual ones for studying the Steenrod algebra. In particular, the operations are constructed using higher symmetries of the shuffle map and their “Adem relations” are computed using the transfer map in the cohomology of symmetric groups.