{
  "id": "math/0603197",
  "version": "v2",
  "published": "2006-03-08T18:26:18.000Z",
  "updated": "2006-05-19T00:33:37.000Z",
  "title": "Commuting Elements and Spaces of Homomorphisms",
  "authors": [
    "Alejandro Adem",
    "Frederick R. Cohen"
  ],
  "comment": "Revised version correcting homology calculations and a few minor points",
  "categories": [
    "math.AT"
  ],
  "abstract": "This article records basic topological, as well as homological properties of the space of homomorphisms Hom(L,G) where L is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If L is a free abelian group of rank equal to n, then Hom(L,G) is the space of ordered n-tuples of commuting elements in G. If G=SU(2), a complete calculation of the cohomology of these spaces is given for n=2, 3. An explicit stable splitting of these spaces is also obtained, as a special case of a more general splitting.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-05-19T00:33:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "55N15",
      "55R50"
    ],
    "keywords": [
      "commuting elements",
      "free abelian group",
      "special case",
      "homomorphisms hom",
      "finitely generated discrete group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3197A"
    }
  }
}