Ravenel-Wilson Hopf Ring Methods in C₂-Equivariant Homotopy Theory and the HF₂-Homology of C₂-Equivariant Eilenberg-MacLane Spaces

This thesis extends Ravenel-Wilson Hopf ring techniques to C₂-equivariant homotopy theory. Our main application and motivation for introducing these methods is a computation of the RO(C₂)-graded homology of C₂-equivariant Eilenberg-MacLane spaces. The result we obtain for C₂-equivariant Eilenberg-MacLane spaces associated to the constant Mackey functor F₂ gives a C₂-equivariant analogue of the classical computation due to Serre at the prime 2. 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 E²-page given in terms of a twisted Tor functor.