$C_2$-equivariant Homology Operations: Results and Formulas

TL;DR

This paper presents corrected and expanded formulas for power operations and Adem relations in $C_2$-equivariant Bredon homology with $F_2$ coefficients, advancing the understanding of equivariant homology operations.

Contribution

It provides revised and extended results on power operations and Adem relations in $C_2$-equivariant homology, incorporating new proofs based on equivariant higher algebra.

Findings

Corrected formulas for power operations

Expanded Adem relations in $C_2$-equivariant Bredon homology

Framework for future proofs using equivariant higher algebra

Abstract

In this note we state corrected and expanded versions of our previous results on power operations for $C_2$-equivariant Bredon homology with coefficients in the constant Mackey functor on $\mathbb{F}_2$. In particular, we give a version of the Adem relations. The proofs rely on certain results in equivariant higher algebra which we will supply in a longer version of this paper.