\(C_2\)-equivariant topological modular forms

Abstract

We compute the homotopy groups of the \(C_2\) fixed points of equivariant topological modular forms at the prime 2 using the descent spectral sequence. We then show that as a \({\mathrm {TMF}}\)-module, it is isomorphic to the tensor product of \({\mathrm {TMF}}\) with an explicit finite cell complex.