Odd primary homotopy types of the gauge groups of exceptional Lie groups

TL;DR

This paper classifies the p-local homotopy types of gauge groups of principal G-bundles over S^4 for exceptional Lie groups G, revealing detailed structure except for one specific case.

Contribution

It provides a comprehensive classification of gauge group homotopy types for exceptional Lie groups, extending previous results to new cases.

Findings

Complete classification for most exceptional Lie groups

Identification of the unique unresolved case for (E_7,5)

Advancement in understanding gauge group homotopy structures

Abstract

The $p$-local homotopy types of gauge groups of principal $G$-bundles over $S^4$ are classified when $G$ is a compact connected exceptional Lie group without $p$-torsion in homology except for $(G,p)=(\mathrm{E}_7,5)$.