{
  "id": "1106.1134",
  "version": "v2",
  "published": "2011-06-06T18:01:33.000Z",
  "updated": "2011-06-13T16:18:44.000Z",
  "title": "Around a conjecture by R. Connelly, E. Demaine, and G. Rote",
  "authors": [
    "Alexander Igamberdiev",
    "Gaiane Panina"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "Denote by $M(P)$ the configuration space of a planar polygonal linkage, that is, the space of all possible planar configurations modulo congruences, including configurations with self-intersections. A particular interest attracts its subset $M^o(P) \\subset M(P)$ of all configurations \\emph{without} self-intersections. R. Connelly, E. Demaine, and G. Rote proved that $M^o(P)$ is contractible and conjectured that so is its closure $\\bar{M^o(P)}$. We disprove this conjecture by showing that a special choice of $P$ makes the homologies $H_k(\\bar{M^o(P)})$ non-trivial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-13T16:18:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M99"
    ],
    "keywords": [
      "conjecture",
      "planar configurations modulo congruences",
      "planar polygonal linkage",
      "special choice",
      "interest attracts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1134I"
    }
  }
}