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

Abstract

Let $G$ be a compact connected simple Lie group of type $(n_{1},\,\ldots,\,n_{l})$ , where $n_{1}<\cdots < n_{l}$ . Let $\mathcal {G}_k$ be the gauge group of the principal $G$ -bundle over $S^{4}$ corresponding to $k\in \pi _3(G)\cong \mathbb {Z}$ . We calculate the mod- $p$ homology of the classifying space $B\mathcal {G}_k$ provided that $n_{l}< p-1$ .