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arXiv · 1810.04771

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

Daisuke Kishimoto·Stephen Theriault
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Abstract

Let $G$ be a simply-connected, simple compact Lie group of type $\{n_{1},\ldots,n_{\ell}\}$, 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 $k$.

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Daisuke Kishimoto, Stephen Theriault. 2018-10-10. The mod-$p$ homology of the classifying spaces of certain gauge groups. https://arxiv.org/abs/1810.04771

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