Computational Motivic and Equivariant Homotopy Theory

The PI proposes to continue his joint work with Dan Isaksen on computations in the motivic and Z=2-equivariant stable homotopy groups of spheres. The computation of mo- tivic stable homotopy groups over C is fairly similar to that of classical stable homotopy groups. From there, the Bockstein spectral sequence recovers the motivic stable homo- topy groups over R. Finally, accounting for the \negative cone" in the Z=2-equivariant homology of a point yields the equivariant stable homotopy groups. The PI proposes to continue to investigate the presentation of G-spectra as spectral Mackey functors. A number of tools that figure centrally in applications, such as equivari- antly commutative multiplications, norm maps, and geometric fixed points, are not well understood in this model of G-spectra.