Homotopy types of gauge groups over non-simply-connected closed 4-manifolds

Tse Leung So

Published 2016-09-08Version 1

Let $G$ be a simply-connected simple compact Lie group and let $M$ be an orientable smooth closed 4-manifold. In this paper we calculate the homotopy type of the suspension of $M$ and the homotopy types of the gauge groups of principal $G$-bundles over $M$ when $\pi_1(M)$ is: (1)~a free group $\mathbb{Z}^{*m}$, (2) a cyclic group $\mathbb{Z}_{p^r}$ where $p$ is an odd prime, or (3) a free product of the previous two types.