Fundamental group of moduli of principal bundles on curves

Abstract

Let $X$ be a compact connected Riemann surface of genus at least two, and let $G$ be a connected semisimple affine algebraic group defined over $\mathbb{C}$. For any $\delta \in {\pi }_1(G)$, we prove that the moduli space of semistable principal $G$--bundles over $X$ of topological type $\delta$ is simply connected. In contrast, the fundamental group of the moduli stack of principal $G$--bundles over $X$ of topological type $\delta$ is shown to be isomorphic to $H^1(X,{\pi }_1(G))$.

Many changes, to appear in Geometriae Dedicata

References in corpus (1)

• Fundamental Groups of Character Varieties: Surfaces and Tori

Cited by in corpus (1)

• Etale Fundamental group of moduli of torsors under Bruhat-Tits group scheme over a curve