Refined gauge group decompositions

Abstract

Let $G$ be a simply connected, compact Lie group, let $P\to S^4$ be a principal $G$-bundle, and let $\mathcal{G}\left(P\right)$ be the gauge group of this bundle. When $G$ is a matrix group and $p$ is an odd prime, we use new methods to improve on the $p$-local homotopy decompositions of $\mathcal{G}\left(P\right)$ appearing in separate work of the first two authors and the third author.