The Homotopy Types of $SU(4)$-Gauge Groups

Abstract

Let ${\mathcal{G}}_k$ be the gauge group of the principal $SU(4)$-bundle over $S^4$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$-local homotopy equivalence $\Omega {\mathcal{G}}_k\simeq \Omega {\mathcal{G}}_{k^{\prime }}$ if and only if $(60,k)=(60,k^{\prime })$.

arXiv comment17 pages