Computing the abelian heap of unpointed stable homotopy classes of maps

TL;DR

This paper introduces a simplified algorithm for computing unpointed stable homotopy classes of maps by leveraging an abelian heap structure, extending previous work on equivariant fibrewise maps.

Contribution

The paper presents a novel simplification of existing computations by utilizing the abelian heap structure on homotopy classes, which was not previously exploited.

Findings

Simplified computation algorithm for unpointed stable homotopy classes

Use of abelian heap structure to facilitate calculations

Extension of previous equivariant fibrewise map results

Abstract

An algorithmic computation of the set of unpointed stable homotopy classes of equivariant fibrewise maps was described in a recent paper of the author and his collaborators. In the present paper, we describe a simplification of this computation that uses an abelian heap structure on this set that was observed in another paper of the author. A heap is essentially a group without a choice of its neutral element; in addition, we allow it to be empty.