{
  "id": "1609.06436",
  "version": "v1",
  "published": "2016-09-21T06:52:07.000Z",
  "updated": "2016-09-21T06:52:07.000Z",
  "title": "Fundamental group of moduli of principal bundles on curves",
  "authors": [
    "Indranil Biswas",
    "Swarnava Mukhopadhyay",
    "Arjun Paul"
  ],
  "categories": [
    "math.AG",
    "math.AT",
    "math.GT"
  ],
  "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 $H^1(X, \\pi_1({G}))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-21T06:52:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D23",
      "14D20",
      "14H30"
    ],
    "keywords": [
      "fundamental group",
      "principal bundles",
      "connected semisimple affine algebraic group",
      "compact connected riemann surface",
      "topological type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}