Power operations for $\text{H}{\underline{\mathbb{F}}}_2$ and a cellular construction of $\text{BP}\mathbf{R}$

Abstract

We study some power operations for ordinary $C_2$-equivariant homology with coefficients in the constant Mackey functor ${\underline{\mathbb{F}}}_2$. In addition to a few foundational results, we calculate the action of these power operations on a $C_2$-equivariant dual Steenrod algebra. As an application, we give a cellular construction of the $C_2$ equivariant Brown-Peterson spectrum $\text{BP}\mathbf{R}$ and deduce its slice tower.

arXiv commentSecond version has minor corrections. Submitted. Supported by NSF grant DGE-1324585

Cited by in corpus (1)

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