{
  "id": "1807.09947",
  "version": "v1",
  "published": "2018-07-26T04:00:15.000Z",
  "updated": "2018-07-26T04:00:15.000Z",
  "title": "Motion planning in connected sums of real projective spaces",
  "authors": [
    "Daniel C. Cohen",
    "Lucile Vandembroucq"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "The topological complexity ${\\sf TC}(X)$ is a homotopy invariant of a topological space $X$, motivated by robotics, and providing a measure of the navigational complexity of $X$. The topological complexity of a connected sum of real projective planes, that is, a high genus nonorientable surface, is known to be maximal. We use algebraic tools to show that the analogous result holds for connected sums of higher dimensional real projective spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-26T04:00:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55S40",
      "55M30",
      "55N25",
      "70Q05"
    ],
    "keywords": [
      "connected sum",
      "motion planning",
      "higher dimensional real projective spaces",
      "high genus nonorientable surface",
      "topological complexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}