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# Singular $G$-Monopoles on $S^1\times \Sigma$

Published:2016-05-04
Printed: Oct 2016
• Benjamin H. Smith,
Department of Mathematics and Statistics, McGill University, Montréal, QC
 Format: LaTeX MathJax PDF

## Abstract

This article provides an account of the functorial correspondence between irreducible singular $G$-monopoles on $S^1\times \Sigma$ and $\vec{t}$-stable meromorphic pairs on $\Sigma$. A theorem of B. Charbonneau and J. Hurtubise is thus generalized here from unitary to arbitrary compact, connected gauge groups. The required distinctions and similarities for unitary versus arbitrary gauge are clearly outlined and many parallels are drawn for easy transition. Once the correspondence theorem is complete, the spectral decomposition is addressed.
 Keywords: connection, curvature, instanton, monopole, stability, Bogomolny equation, Sasakian geometry, cameral covers
 MSC Classifications: 53C07 - Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20] 14D20 - Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}

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