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Quaternionic monopoles


Okonek, C; Teleman, A (1995). Quaternionic monopoles. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 321(5):601-606.

Abstract

We present the simplest non-abelian version of Seiberg-Witten theory: quaternionic monopoles. On Kähler surfaces the quaternionic monopole equations decouple and lead to a projective vortex equation. This vortex equation comes from a moment map and gives rise to a new stability concept for holomorphic pairs. The moduli spaces of quaternionic monopoles on Kähler surfaces decompose into two closed subspaces, both naturally isomorphic with moduli spaces of canonically stable pairs. These components intersect along Donaldson's instanton space and can be compactified with spaces associated with (abelian) Seiberg-Witten monopoles [E. Witten, Math. Res. Lett. 1 (1994), no. 6, 769--796]

Abstract

We present the simplest non-abelian version of Seiberg-Witten theory: quaternionic monopoles. On Kähler surfaces the quaternionic monopole equations decouple and lead to a projective vortex equation. This vortex equation comes from a moment map and gives rise to a new stability concept for holomorphic pairs. The moduli spaces of quaternionic monopoles on Kähler surfaces decompose into two closed subspaces, both naturally isomorphic with moduli spaces of canonically stable pairs. These components intersect along Donaldson's instanton space and can be compactified with spaces associated with (abelian) Seiberg-Witten monopoles [E. Witten, Math. Res. Lett. 1 (1994), no. 6, 769--796]

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1995
Deposited On:29 Nov 2010 16:28
Last Modified:06 Dec 2017 21:06
Publisher:Elsevier
ISSN:0151-0509
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1356561
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0842.53051

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