The H𝔽2–homology of C2–equivariantEilenberg–Mac Lane spaces

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-Mac Lane spaces.The result we obtain for C 2 -equivariant Eilenberg-Mac Lane spaces associated to the constant Mackey functor 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-Mac Lane spaces and suggest the existence of another twisted bar spectral sequence with E 2 -page given in terms of a twisted Tor functor.55P91; 55N91, 55P20 1. Introduction 4487 2. Classical Ravenel-Wilson Hopf ring methods 4494 3. Equivariant preliminaries 4497 4. Bar and twisted bar constructions 4499 5. Multiplicative structures on C 2 -equivariant Eilenberg-Mac Lane spaces 4501 6. Bar and twisted bar spectral sequence computations 4505 7.