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Singular G-Monopoles on S1 × Σ

Published online by Cambridge University Press:  20 November 2018

Benjamin H. Smith
Benjamin H. Smith*
Affiliation:
Department of Mathematics and Statistics, McGill University, Montréal, QC e-mail: bh2smith@gmail.com
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Abstract

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This article provides an account of the functorial correspondence between irreducible singular $G$-monopoles on ${{S}^{1}}\,\times \,\sum $ and $\vec{t}$-stable meromorphic pairs on $\sum $. 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

53C0714D20connectioncurvatureinstantonmonopolestabilityBogomolny equationSasakian geometrycameral covers
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 5 , 01 October 2016 , pp. 1096 - 1119
Copyright
Copyright © Canadian Mathematical Society 2016

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