Morse theory for the space of Higgs G-bundles

Biswas, Indranil ; Wilkin, Graeme (2010) Morse theory for the space of Higgs G-bundles Geometriae Dedicata . ISSN 0046-5755

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Fix a C principal G-bundle E0G on a compact connected Riemann surface X, where G is a connected complex reductive linear algebraic group. We consider the gradient flow of the Yang-Mills-Higgs functional on the cotangent bundle of the space of all smooth connections on E0G. We prove that this flow preserves the subset of Higgs G-bundles, and, furthermore, the flow emanating from any point of this subset has a limit. Given a Higgs G-bundle, we identify the limit point of the integral curve passing through it. These generalize the results of the second named author on Higgs vector bundles.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Higgs Bundle; Principal Bundle; Morse Flow
ID Code:3641
Deposited On:18 Oct 2010 10:15
Last Modified:27 Jan 2011 05:42

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