$C_2$-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.

v3: Published in Journal of Homotopy and Related Structures v2: Added appendix on connective equivariant tmf. Minor adjustments

References in corpus (3)

• Affineness and chromatic homotopy theory
• Motivic modular forms from equivariant stable homotopy theory
• Topological Modular Forms of Level 3