论文标题
轻柔地介绍非亚伯杂货
A Gentle Introduction to the Non-Abelian Hodge Correspondence
论文作者
论文摘要
我们的目的是对非亚伯杂货的对应关系进行教学介绍，这是代数，几何结构和复杂几何形状之间的桥梁。这些对应关系将基本群体（角色多样性）的表示与全体形态束理论联系起来。 我们专注于动机，关键思想，概念和应用之间的联系。除其他外，我们讨论了Riemann-Hilbert对应关系，Goldman通过Atiyah-Bott降低，Narasimhan--Seshadri定理，Higgs捆绑，谐波捆绑包和Hyperkähhler歧管。
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 hyperkähler manifolds.
