Mod 2 power operations revisited

Wilson, Dylan

doi:10.2140/agt.2023.23.2993

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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 $𝔼_{\infty}$ –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

Open Access made possible by participating institutions via Subscribe to Open.

Volume 23, issue 7 (2023)