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Mod $2$ power operations revisited

Dylan Wilson
Algebraic & Geometric Topology 23 (2023) 2993–3014
DOI: 10.2140/agt.2023.23.2993
Abstract

In this mostly expository note we take advantage of homotopical and algebraic advances to give a modern account of power operations on the mod 2 homology of 𝔼∞–ring spectra. The main advance is a quick proof of the Adem relations utilizing the Tate-valued Frobenius as a homotopical incarnation of the total power operation. We also give a streamlined derivation of the action of power operations on the dual Steenrod algebra.

Keywords
power operations, Dyer–Lashof operations, Steenrod algebra, Nishida relations, Adem relations, Tate Frobenius
Mathematical Subject Classification
Primary: 55P43, 55S12
References
Publication
Received: 26 November 2020
Revised: 5 February 2022
Accepted: 15 May 2022
Published: 26 September 2023
Authors
Dylan Wilson
Department of Mathematics
West Virginia University
Morgantown, WV
United States
© 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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