Fundamental group of moduli of principal bundles on curves

Indranil Biswas; Swarnava Mukhopadhyay; Arjun Paul

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arXiv · 1609.06436

Fundamental group of moduli of principal bundles on curves

Indranil Biswas·Swarnava Mukhopadhyay·Arjun Paul

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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 $H^1(X, \pi_1({G}))$.

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BibTeX RIS

Indranil Biswas, Swarnava Mukhopadhyay, Arjun Paul. 2016-09-21. Fundamental group of moduli of principal bundles on curves. https://arxiv.org/abs/1609.06436

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