$RO(C_2)$-graded Cohomology of $C_2$-equivariant Eilenberg-Mac Lane spaces

TL;DR

This paper computes the $RO(C_2)$-graded cohomology of certain $C_2$-equivariant Eilenberg-Mac Lane spaces, providing tools to connect equivariant algebraic topology frameworks like the lambda algebra and Adams spectral sequences.

Contribution

It introduces explicit calculations of $RO(C_2)$-graded cohomology for $K(, n+
)$ spaces, linking them to key algebraic topology tools.

Findings

Explicit $RO(C_2)$-graded cohomology calculations for $K(, n+
)$.

Establishment of relations between equivariant lambda algebra and Adams spectral sequences.

Applications to understanding equivariant unstable homotopy theory.

Abstract

In this paper, we calculate $RO(C_2)$-graded cohomology of $C_2$-equivariant Eilenberg-Mac Lane spaces $K(\underline{Z/2}, n+\sigma)$ for $n\geq 0$. These can be used to give the relation between equivariant lambda algebra and equivariant Adams resolution and equivariant unstable Adams spectral sequence, which are defined in author`s dissertation.