Non-abelian Hodge correspondence and moduli spaces of flat bundles on Sasakian manifolds with fixed basic structures

2024/10/25 by Hisashi Kasuya, Kasuya, Hisashi
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2410.19281

Abstract

We show that the moduli space of simple flat bundles over a compact Sasakian manifold is a finite disjoint union of moduli spaces of simple flat bundles with fixed basic structures. This gives a detailed description of the non-abelian Hodge correspondence on a compact Sasakian manifold at the level of moduli spaces. As an application, we give an analogue of Hitchin's properness of maps defined by the coefficients of the characteristic polynomial of Higgs fields.

Related

• Higgs bundles and flat connections over compact Sasakian manifolds, II: quasi-regular bundles
• A Gentle Introduction to the Non-Abelian Hodge Correspondence
• Moduli spaces in p-adic non-abelian Hodge theory
• Higgs bundles on Sasakian manifolds
• Hodge structure on the cohomology of the moduli space of Higgs bundles