The $H{\underline{\mathbb{F}}}_2$-homology of $C_2$-equivariant Eilenberg-MacLane spaces

Abstract

We extend Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation is a computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The result we obtain for $C_2$-equivariant Eilenberg-MacLane spaces associated to the constant Mackey functor ${\underline{\mathbb{F}}}_2$ gives a $C_2$-equivariant analogue of the classical computation due to Serre. We also investigate a twisted bar spectral sequence computing the homology of these equivariant Eilenberg-MacLane spaces and suggest the existence of another twisted bar spectral sequence with $E^2$-page given in terms of a twisted Tor functor.

Extends prior computational result from some (Theorems 5.2 and 6.4) to all $C_2$-equivariant Eilenberg-MacLane spaces associated to the constant Mackey functor ${\underline{\mathbb{F}}}_2$ (Theorem 6.3) , 31 pages, 10 figures, Comments welcome

References in corpus (1)

• Hopf algebra structure on topological Hochschild homology