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Morse theory for the space of Higgs G–bundles

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JournalGeometriae Dedicata
DatePublished - 1 Feb 2010
Issue number1
Volume149
Number of pages15
Pages (from-to)189-203
Original languageEnglish

Abstract

Fix a smooth principal G–bundle 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 this bundle. 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.

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