UBC Topology Seminar: Krishanu Sankar

In episode 2 of the series, I will turn my attention to the setting of G-equivariant stable homotopy theory, where G is an abelian p-group. Analogous to the classical case, we can use symmetric powers of the equivariant sphere to filter H\underline{\F}_p, and the cofibers are Steinberg summands of equivariant classifying spaces. We then study how the cells of these spaces split after smashing with H\underline{\F}_p in the case G=C_p. When p=2, the result is a decomposition of H\underline{\F}_2 \sm H\underline{\F}_2 whose generators correspond to representation spheres, while at odd primes, we see something more unusual.