Singular G-Monopoles on S 1 × Σ

Smith, Benjamin H.

Canadian journal of mathematics, Tome 68 (2016) no. 5, pp. 1096-1119

Résumé

This article provides an account of the functorial correspondence between irreduciblesingular $G$ -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.

Détail

DOI : 10.4153/CJM-2016-010-2

Mots-clés : 53C07, 14D20, connection, curvature, instanton, monopole, stability, Bogomolny equation, Sasakian geometry, cameral covers

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