Volume 24, issue 6 (2020)

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Eilenberg–Mac Lane spectra as equivariant Thom spectra

Jeremy Hahn and Dylan Wilson

Geometry & Topology 24 (2020) 2709–2748
DOI: 10.2140/gt.2020.24.2709

We prove that the G–equivariant mod p Eilenberg–Mac Lane 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 C2. We also establish a construction of H¯(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 nonequivariant H 𝔽p arises as the Thom spectrum of a more than double loop map.

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Thom spectrum, equivariant, Mahowald, Eilenberg–MacLane
Mathematical Subject Classification 2010
Primary: 55P43, 55P91
Received: 1 May 2018
Revised: 19 November 2019
Accepted: 29 December 2019
Published: 29 December 2020
Proposed: Mark Behrens
Seconded: Haynes R Miller, Ralph Cohen
Jeremy Hahn
Mathematics Department
Massachusetts Institute of Technology
Cambridge, MA
United States
Dylan Wilson
Department of Mathematics
Harvard University
Cambridge, MA
United States