{
  "id": "0704.1922",
  "version": "v4",
  "published": "2007-04-16T19:49:19.000Z",
  "updated": "2008-08-04T00:54:42.000Z",
  "title": "Relative Rigidity, Quasiconvexity and C-Complexes",
  "authors": [
    "Mahan Mj"
  ],
  "comment": "23pgs, v3: Relative rigidity proved for relatively hyperbolic groups and higher rank symmetric spaces, v4: final version incorporating referee's comments. To appear in \"Algebraic and Geometric Topology\"",
  "journal": "Algebraic & Geometric Topology 8 (2008) 1691-1716",
  "doi": "10.2140/agt.2008.8.1691",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We introduce and study the notion of relative rigidity for pairs $(X,\\JJ)$ where 1) $X$ is a hyperbolic metric space and $\\JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $\\JJ$ the collection of parabolics 3) $X$ is a higher rank symmetric space and $\\JJ$ an equivariant collection of maximal flats Relative rigidity can roughly be described as upgrading a uniformly proper map between two such $\\JJ$'s to a quasi-isometry between the corresponding $X$'s. A related notion is that of a $C$-complex which is the adaptation of a Tits complex to this context. We prove the relative rigidity of the collection of pairs $(X, \\JJ)$ as above. This generalises a result of Schwarz for symmetric patterns of geodesics in hyperbolic space. We show that a uniformly proper map induces an isomorphism of the corresponding $C$-complexes. We also give a couple of characterizations of quasiconvexity. of subgroups of hyperbolic groups on the way.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-08-04T00:54:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "22E40",
      "57M50"
    ],
    "keywords": [
      "quasiconvexity",
      "hyperbolic group",
      "c-complexes",
      "higher rank symmetric space",
      "maximal flats relative rigidity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.1922M"
    }
  }
}