Quasi-elliptic cohomology of 4-spheres

TL;DR

This paper computes the quasi-elliptic cohomology of 4-spheres under specific finite group actions, providing insights into its role as an approximation to equivariant 4-th Cohomotopy relevant to M-brane charges in M-theory.

Contribution

It offers the first explicit calculations of quasi-elliptic cohomology for 4-spheres with finite group actions, connecting mathematical theory to M-brane charge classification.

Findings

Computed quasi-elliptic cohomology for 4-spheres with finite subgroup actions.

Identified key isotropy groups relevant to M-brane configurations.

Provided evidence supporting the conjecture relating quasi-elliptic cohomology to equivariant 4-th Cohomotopy.

Abstract

Quasi-elliptic cohomology is conjectured by Sati and Schreiber as a particularly suitable approximation to equivariant 4-th Cohomotopy, which classifies the charges carried by M-branes in M-theory in a way that is analogous to the traditional idea that complex K-theory classifies the charges of D-branes in string theory. In this paper we compute quasi-elliptic cohomology of 4-spheres under the action by some finite subgroups that are the most interesting isotropy groups where the M5-branes may sit.