Morse theory for the space of Higgs G-bundles

Abstract

Fix a $C^{\infty }$ principal $G$--bundle $E_G^0$ 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 $E_G^0$. 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.

16 pages, to appear Geometriae Dedicata

References in corpus (2)

• Yang-Mills equation for stable Higgs sheaves
• Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles