Morse theory for the space of Higgs G–bundles

By Indranil Biswas, Graeme Wilkin. 2006

54 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b3919aedc0a325cea0cbecfcd383eab72ae7a4e2