The slices of $S^n \wedge H\underline{\mathbb{Z}}$ for cyclic $p$-groups

TL;DR

This paper computes the slice tower for spectra of the form $S^n igwedge H\underline{\mathbb{Z}}$ in the equivariant setting for cyclic p-groups, extending understanding of slice filtrations in equivariant stable homotopy theory.

Contribution

It explicitly determines the slice tower for all such spectra when the group is a cyclic p-group and p is an odd prime, a case previously not fully understood.

Findings

Complete slice towers are identified for the spectra considered.

The results extend the known cases of slice filtrations in equivariant spectra.

Provides tools for future computations in equivariant homotopy theory.

Abstract

The slice filtration is a filtration of equivariant spectra. While the tower is analogous to the Postnikov tower in the nonequivariant setting, complete slice towers are known for relatively few $G$-spectra. In this paper, we determine the slice tower for all $G$-spectra of the form $S^n \wedge H\underline{\mathbb{Z}}$ where $n\geq 0$ and $G$ is a cyclic $p$-group for $p$ an odd prime.