{
  "id": "1407.6815",
  "version": "v2",
  "published": "2014-07-25T08:53:38.000Z",
  "updated": "2015-02-17T10:28:59.000Z",
  "title": "Universality theorems for linkages in homogeneous surfaces",
  "authors": [
    "Mickaël Kourganoff"
  ],
  "comment": "53 pages. arXiv admin note: substantial text overlap with arXiv:1401.1050",
  "categories": [
    "math.MG",
    "math.DG",
    "math.GT"
  ],
  "abstract": "A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of linkages in the (Lorentz-)Minkowski plane, in the hyperbolic plane and in the sphere. We also give a proof of a differential universality theorem in the Minkowski plane and in the hyperbolic plane: for any compact manifold M, there is a linkage whose configuration space is diffeomorphic to the disjoint union of a finite number of copies of M. In the Minkowski plane, it is also true for any manifold M which is the interior of a compact manifold with boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-25T08:53:38.000Z",
      "title": "Universality theorems for linkages in the hyperbolic plane",
      "abstract": "A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of linkages in the hyperbolic plane. We also give a proof of a differential universality theorem in the hyperbolic plane: for any compact manifold M, there is a linkage which has a configuration space diffeomorphic to the disjoint union of a finite number of copies of M.",
      "comment": "13 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-17T10:28:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51M09",
      "14P05",
      "14P10",
      "57R99",
      "51F99",
      "53B30"
    ],
    "keywords": [
      "hyperbolic plane",
      "partial configuration space",
      "configuration space diffeomorphic",
      "differential universality theorem",
      "compact manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.6815K"
    }
  }
}