Morse theory for the space of Higgs G-bundles

Details Morse theory for the space of Higgs G-bundles Morse theory for the space of Higgs G-bundles

2010-02-05

arxiv.org/abs/1002.1108v1

Mathematics

Differential Geometry

16 pages, to appear Geometriae Dedicata

Scientific paper

Fix a $C^\infty$ 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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