Fundamental group of moduli of principal bundles on curves

2016/09/21 by Biswas, Indranil, Mukhopadhyay, Swarnava, Paul, Arjun · 1 citation
#14D20 #14D23 #14H30 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1609.06436

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 δ∈ π₁(G), we prove that the moduli space of semistable principal G--bundles over X of topological type δ is simply connected. In contrast, the fundamental group of the moduli stack of principal G--bundles over X of topological type δ is shown to be isomorphic to H¹(X, π₁(G)).

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• Brauer group of moduli of parabolic symplectic bundles

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