{
  "id": "1510.07984",
  "version": "v1",
  "published": "2015-10-27T16:53:30.000Z",
  "updated": "2015-10-27T16:53:30.000Z",
  "title": "Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints",
  "authors": [
    "Pavle V. M. Blagojević",
    "Florian Frick",
    "Günter M. Ziegler"
  ],
  "comment": "6 pages. This manuscript subsumes arxiv:1502.00947 and arxiv:1411.4417",
  "categories": [
    "math.CO",
    "math.AT",
    "math.MG"
  ],
  "abstract": "Using the authors' 2014 \"constraints method,\" we give a short proof for a 2015 result of Dobbins on representations of a point in a polytope as the barycenter of points in a skeleton, and show that the \"r-fold Whitney trick\" of Mabillard and Wagner (2014/2015) implies that the Topological Tverberg Conjecture for r-fold intersections fails dramatically for all r that are not prime powers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-27T16:53:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A35",
      "55S35",
      "51M04",
      "51M20",
      "52B11"
    ],
    "keywords": [
      "topological tverberg conjecture",
      "polytope skeleta",
      "barycenter",
      "counterexamples",
      "r-fold intersections fails"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007984B"
    }
  }
}