{
  "id": "1411.0902",
  "version": "v1",
  "published": "2014-11-04T13:31:11.000Z",
  "updated": "2014-11-04T13:31:11.000Z",
  "title": "Resolutions of CAT(0) cube complexes and accessibility properties",
  "authors": [
    "Benjamin Beeker",
    "Nir Lazarovich"
  ],
  "comment": "17 pages, 10 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "In [4], Dunwoody defined resolutions for finitely presented group actions on simplicial trees, that is, an action of the group on a tree with smaller edge and vertex stabilizers. He, moreover, proved that the size of the resolution is bounded by a constant depending only on the group. Extending Dunwoody's definition of patterns we construct resolutions for group actions on a general finite dimensional CAT(0) cube complex. In dimension two, we bound the number of hyperplanes of this resolution. We apply this result for surfaces and 3-manifolds to bound collections of codimension-1 submanifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-04T13:31:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20E08"
    ],
    "keywords": [
      "cube complexes",
      "accessibility properties",
      "general finite dimensional cat",
      "group actions",
      "smaller edge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.0902B"
    }
  }
}