Homotopy types of gauge groups related to $S^3$-bundles over $S^4$

Ingrid Membrillo-Solis

Published 2017-07-21Version 1

Let $M$ be the total space of an $S^3$-bundle over $S^4$ and $G$ be a simply connected simple compact Lie group. If the integral homology of $M$ is torsion free we describe the homotopy type of the gauge groups over $M$ as products of recognisable spaces. For any manifold $M$ with non torsion free homology, we give a $p$-local homotopy decomposition, $p\geq 5$, of the loop space of the gauge groups.