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Morse theory for the space of Higgs G–bundles

Author:
Indranil Biswas and Graeme Wilkin  


Journal:
Geometriae Dedicata


Issue Date:
2010


Abstract(summary):

Fix a C ∞ principal G–bundle E0G{E^0_G} 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{E^0_G}. 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.


Page:
189-203


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