A Gentle Introduction to the Non-Abelian Hodge Correspondence
Differential Geometry
2023-04-24 v2 Mathematical Physics
Algebraic Geometry
math.MP
Symplectic Geometry
Abstract
We aim at giving a pedagogical introduction to the non-abelian Hodge correspondence, a bridge between algebra, geometric structures and complex geometry. The correspondence links representations of a fundamental group, the character variety, to the theory of holomorphic bundles. We focus on motivations, key ideas, links between the concepts and applications. Among others we discuss the Riemann--Hilbert correspondence, Goldman's symplectic structure via the Atiyah--Bott reduction, the Narasimhan--Seshadri theorem, Higgs bundles, harmonic bundles and hyperk\"ahler manifolds.
Keywords
Cite
@article{arxiv.2208.05940,
title = {A Gentle Introduction to the Non-Abelian Hodge Correspondence},
author = {Alexander Thomas},
journal= {arXiv preprint arXiv:2208.05940},
year = {2023}
}