{
  "id": "1401.0531",
  "version": "v3",
  "published": "2014-01-02T20:57:35.000Z",
  "updated": "2015-05-12T09:45:04.000Z",
  "title": "Equivariant Alexandrov geometry and orbifold finiteness",
  "authors": [
    "John Harvey"
  ],
  "comment": "25 pages, in v2 citation for Theorem 2.13 was corrected, in this version the material of arXiv:1401.0739 was incorporated. The combined article has been published in the Journal of Geometric Analysis",
  "doi": "10.1007/s12220-015-9614-6",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in the equivariant Gromov--Hausdorff topology, then the limit space is equivariantly homeomorphic to spaces in the tail of the sequence. As a consequence, the class of Riemannian orbifolds of dimension $n$ defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is finite up to orbifold homeomorphism.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-05T21:43:34.000Z",
      "title": "Equivariant stability of Alexandrov spaces",
      "abstract": "Let a compact Lie group act isometrically on a non-collapsing sequence of Alexandrov spaces with fixed dimension and diameter bounded above. If the sequence of actions is equicontinuous and converges in the equivariant Gromov--Hausdorff topology, then the limit space is equivariantly homeomorphic to spaces in the tail of the sequence.",
      "comment": "12 pages, corrected citation for Theorem 2.13",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-05-12T09:45:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "53C20",
      "51K10"
    ],
    "keywords": [
      "alexandrov spaces",
      "equivariant stability",
      "compact lie group act",
      "equivariant gromov-hausdorff topology",
      "limit space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0531H"
    }
  }
}