A $C_2$-equivariant analog of Mahowald's Thom spectrum theorem

TL;DR

This paper establishes a $C_2$-equivariant version of Mahowald's Thom spectrum theorem, showing that a specific equivariant Eilenberg-MacLane spectrum is equivalent to a Thom spectrum over a certain loop space.

Contribution

It introduces a $C_2$-equivariant analog of Mahowald's theorem, expanding the understanding of equivariant stable homotopy theory.

Findings

Equivalence between the $C_2$-equivariant Eilenberg-MacLane spectrum and a Thom spectrum.

Identification of the Thom spectrum over ${ m ho^ ho S^{ ho + 1}}$ as representing the constant Mackey functor.

Advancement in equivariant homotopy theory by generalizing classical results.

Abstract

We prove that the $C_2$-equivariant Eilenberg-MacLane spectrum associated to the constant Mackey functor $\underline{\mathbb{F}}_2$ is equivalent to a Thom spectrum over ${\Omega^\rho S^{\rho + 1}}$.