Abstract
Fix a C ∞ principal G–bundle \({E^0_G}\) 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 \({E^0_G}\). 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.
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Biswas, I., Wilkin, G. Morse theory for the space of Higgs G–bundles. Geom Dedicata 149, 189–203 (2010). https://doi.org/10.1007/s10711-010-9476-9
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DOI: https://doi.org/10.1007/s10711-010-9476-9