Klein Four 2-slices and the Slices of $\Sigma^{\pm n}H\underline{\mathbb{Z}}$

TL;DR

This paper characterizes all 2-slices of equivariant spectra over the Klein four-group and describes the slices of integral suspensions of the equivariant Eilenberg-MacLane spectrum for the constant Mackey functor.

Contribution

It provides a complete characterization of 2-slices over the Klein four-group and describes slices of suspensions of a key equivariant spectrum, advancing equivariant stable homotopy theory.

Findings

All 2-slices over the Klein four-group are characterized.

Slices of integral suspensions of $HbZ$ are explicitly described.

The results facilitate computations in equivariant stable homotopy theory.

Abstract

We determine a characterization of all 2-slices of equivariant spectra over the Klein four-group $C_2\times C_2$. We then describe all slices of integral suspensions of the equivariant Eilenberg-MacLane spectrum $H\underline{\mathbb{Z}}$ for the constant Mackey functor over $C_2\times C_2$.