Topology Seminar: Dylan Wilson

We introduce the notion of a spoke algebra, which encodes the data of a $C_p$-equivariant cohomology equipped with a coherent system of norms. This is a generalization of the notion of an ``$\mathbb{E}_{\sigma}$-algebra" for the group $C_2$ and the sign representation $\sigma$. We explain several naturally occurring examples (such as certain mapping spaces) and then describe several applications. The first is a method for delooping a suitably structured space by an irreducible, 2-dimensional $C_p$-representation in two steps. The second is the construction of certain interesting $C_p$-spectra related to the odd primary Kervaire invariant problem using a version of Koszul duality for spoke algebras. This is joint work with Jeremy Hahn.