The slices of quaternionic Eilenberg-Mac Lane spectra

TL;DR

This paper computes the slices and slice spectral sequence of equivariant Eilenberg-Mac Lane spectra for the group Q_8, advancing understanding of their algebraic and homotopical structures.

Contribution

It provides explicit calculations of slices, spectral sequences, and Mackey functors for integral suspensions of equivariant Eilenberg-Mac Lane spectra with group Q_8.

Findings

Computed the slices and slice spectral sequence for the spectra.

Determined the Mackey functors $ ext{pi}_{k ho} H ext{Z}$.

Enhanced understanding of equivariant homotopy theory for Q_8.

Abstract

We compute the slices and slice spectral sequence of integral suspensions of the equivariant Eilenberg-Mac Lane spectra $H\underline{\mathbb{Z}}$ for the group of equivariance $Q_8$. Along the way, we compute the Mackey functors $\underline{\pi}_{k\rho} H\underline{\mathbb{Z}}$.