URegina Topology Seminar: Sarah Petersen

This talk describes an extension of 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.