Computing Equivariant Homotopy with a Splitting Method

TL;DR

This paper introduces a novel splitting method for computing equivariant homotopy groups, enabling calculations for complex groups like D_{2p} and A_5 within the framework of equivariant spectra.

Contribution

The paper presents a new splitting technique based on cofiber sequences to compute equivariant homotopy groups, advancing computational methods in equivariant stable homotopy theory.

Findings

Computed homotopy of Hundal{} for G=D_{2p} and A_5

Developed a splitting method for cofiber sequences in equivariant spectra

Enhanced computational tools for equivariant homotopy groups

Abstract

We develop a new method in the computation of equivariant homotopy, which is based on the splitting of cofiber sequences associated to universal spaces in the category of equivariant spectra. In particular, we use this method to compute the homotopy of $H\underline{\mathbb{Z}}$ for $G=D_{2p}$ and $A_5$.