The mod-$p$ homology of the classifying spaces of certain gauge groups

Abstract

Let $G$ be a simply-connected, simple compact Lie group of type $\{n_1,\dots ,n_{\ell }\}$, where $n_1\le \cdots \le n_{\ell }$. Let ${\mathcal{G}}_k$ be the gauge group of the principal $G$-bundle (namedright{P}{}{S^{4}}) whose isomorphism class is determined by the the second Chern class having value $k\in \mathbb{Z}$. We calculate the mod-$p$ homology of the classifying space $B{\mathcal{G}}_k$ provided that $n_{\ell }<p-1$ and $p$ does not divide $k$.

arXiv comment12 pages