{
  "id": "1301.7616",
  "version": "v3",
  "published": "2013-01-31T13:57:13.000Z",
  "updated": "2014-05-12T20:07:26.000Z",
  "title": "Topology of character varieties of Abelian groups",
  "authors": [
    "C. Florentino",
    "S. Lawton"
  ],
  "comment": "33 pages; version 3: few small changes, one error corrected, one or two additional references; to appear in Topology and its Applications",
  "journal": "Topology and its Applications, Volume 173, 15 August 2014, Pages 32-58",
  "doi": "10.1016/j.topol.2014.05.009",
  "categories": [
    "math.AG",
    "math.GT",
    "math.RT"
  ],
  "abstract": "Let G be a complex reductive algebraic group (not necessarily connected), let K be a maximal compact subgroup, and let A be a finitely generated Abelian group. We prove that the conjugation orbit space Hom(A,K)/K is a strong deformation retract of the GIT quotient space Hom(A,G)//G. As a corollary, we determine necessary and sufficient conditions for the character variety Hom(A,G)//G to be irreducible when G is connected and semisimple. For a general connected reductive G, analogous conditions are found to be sufficient for irreducibility, when A is free abelian.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-12T20:07:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14P25",
      "14L17",
      "14L24",
      "22E46"
    ],
    "keywords": [
      "conjugation orbit space hom",
      "git quotient space hom",
      "maximal compact subgroup",
      "character variety hom",
      "complex reductive algebraic group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.7616F"
    }
  }
}