Odd primary homotopy decompositions of gauge groups

Abstract

We construct $p$–local decompositions of certain gauge groups when $p$ is an odd prime. Specifically, we decompose $SU\left(n\right)$, $Sp\left(n\right)$ and $Spin\left(n\right)$–gauge groups over simply connected $4$–manifolds and $U\left(n\right)$–gauge groups over compact, orientable Riemann surfaces, given certain restrictions on $n$ that depend on $p$.