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

Abstract

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)~${\mathbb{Z}}^{\ast m}$, (2)~$\mathbb{Z}/p^r\mathbb{Z}$, or (3)~${\mathbb{Z}}^{\ast m}\ast ({\ast }_{j=1}^n\mathbb{Z}/p_j^{r_j}\mathbb{Z})$, where $p$ and the $p_j$'s are odd primes.

arXiv comment21 pages; accepted by Glasgow Mathematical Journal