The $RO(\mathcal{K})$-graded homotopy of Klein-four normed Mackey functors

TL;DR

This paper computes the $RO( ext{K})$-graded coefficients of certain equivariant spectra related to the Klein-four group and analyzes their multiplicative structures, advancing understanding of equivariant homotopy theory for Mackey functors.

Contribution

It provides explicit calculations of $RO( ext{K})$-graded coefficients for Hill-Hopkins-Ravenel norms of constant Mackey functors and explores their multiplicative properties.

Findings

Explicit $RO( ext{K})$-graded coefficients computed.

Multiplicative structures of $RO( ext{K})$-graded Tambara functors analyzed.

Enhanced understanding of equivariant homotopy for Klein-four group.

Abstract

We compute the $RO(\mathcal{K})$-graded coefficients of the equivariant Eilenberg-Mac Lane spectrum associated to various Hill-Hopkins-Ravenel norms of the constant-$\mathbb{F}_2$ Mackey functor, where $\mathcal{K}$ is the Klein-four group. Further, we analyze the multiplicative structure of these $RO(\mathcal{K})$-graded Tambara functors.