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

Part of: Quantum field theory; related classical field theories Fiber spaces and bundles

Published online by Cambridge University Press:  19 September 2022

Daisuke Kishimoto  and
Stephen Theriault
Daisuke Kishimoto
Affiliation:
Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan (kishimoto@math.kyushu-u.ac.jp)
Stephen Theriault
Affiliation:
Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom (s.d.theriault@soton.ac.uk)
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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 $n_{l}< p-1$.

Keywords

Gauge groupclassifying spacehomology

MSC classification

Primary: 55R40: Homology of classifying spaces, characteristic classes
Secondary: 81T13: Yang-Mills and other gauge theories
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 6 , December 2023 , pp. 1805 - 1817
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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