The C2-Effective Spectral Sequence for ?C2-Equivariant Connective Real K-Theory

摘要

We construct a C2-equivariant spectral sequence for RO(C2)-graded homotopy groups. The construction is by using the motivic effective slice filtration and the C2-equivariant Betti realization. We apply the spectral sequence to compute the RO(C2)-graded homotopy groups of the completed C2-equivariant connective real K-theory spectrum. The computation reproves the C2-equivariant Adams spectral sequence results by Guillou, Hill, Isaksen and Ravenel.