Mod 2 power operations revisited

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 ${\mathbb{E}}_{\infty }$-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.

20 pages, comments very welcome!

References in corpus (2)

• Stable $\infty$-Operads and the multiplicative Yoneda lemma
• Stable power operations

Cited by in corpus (1)

• Integral Models for Spaces via the Higher Frobenius