Eilenberg-MacLane spectra as equivariant Thom spectra

Abstract

We prove that the $G$-equivariant mod $p$ Eilenberg--MacLane spectrum arises as an equivariant Thom spectrum for any finite, $p$-power cyclic group $G$, generalizing a result of Behrens and the second author in the case of the group $C_2$. We also establish a construction of $\mathrm{H}{\underline{\mathbb{Z}}}_{(p)}$, and prove intermediate results that may be of independent interest. Highlights include constraints on the Hurewicz images of equivariant spectra that admit norms, and an analysis of the extent to which the non-equivariant $\mathrm{H}{\mathbb{F}}_p$ arises as the Thom spectrum of a more than double loop map.

v4: Various errors corrected and new section on pi_1 added. Now published in Geometry and Topology

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Cited by in corpus (6)

• Equivariant nonabelian Poincaré duality and equivariant factorization homology of Thom spectra
• Higher chromatic Thom spectra via unstable homotopy theory
• On the $C_p$-equivariant dual Steenrod algebra
• Parametrized spectra, a low-tech approach
• A Thom Spectrum Model for $C_2$-Integral Brown--Gitler Spectra
• On the Whitehead theorem for nilpotent motivic spaces