{
  "id": "1310.5487",
  "version": "v1",
  "published": "2013-10-21T10:12:44.000Z",
  "updated": "2013-10-21T10:12:44.000Z",
  "title": "Simplicial complexes Alexander dual to boundaries of polytopes",
  "authors": [
    "Anton Ayzenberg"
  ],
  "comment": "18 pages, 9 figures",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "In the paper we treat Gale diagrams in a combinatorial way. The interpretation allows to describe simplicial complexes which are Alexander dual to boundaries of simplicial polytopes and, more generally, to nerve-complexes of general polytopes. This technique and recent results of N.Yu.Erokhovets are combined to prove the following: Buchstaber invariant $s(P)$ of a convex polytope equals 1 if and only if $P$ is a pyramid. In general, we describe a procedure to construct polytopes with $s_R(P)>k$. The construction has purely combinatorial consequences. We also apply Gale duality to the study of bigraded Betti numbers and f-vectors of polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-21T10:12:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "52B35",
      "52B05",
      "13F55",
      "55U10",
      "05C15"
    ],
    "keywords": [
      "simplicial complexes alexander dual",
      "boundaries",
      "treat gale diagrams",
      "convex polytope equals",
      "combinatorial way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5487A"
    }
  }
}