{
  "id": "0908.3448",
  "version": "v2",
  "published": "2009-08-24T14:29:19.000Z",
  "updated": "2009-10-09T08:43:32.000Z",
  "title": "Buchstaber invariants of skeleta of a simplex",
  "authors": [
    "Yukiko Fukukawa",
    "Mikiya Masuda"
  ],
  "journal": "Osaka J. Math. 48 (2011), 549-582",
  "categories": [
    "math.AT"
  ],
  "abstract": "A moment-angle complex $\\mathcal{Z}_K$ is a compact topological space associated with a finite simplicial complex $K$. It is realized as a subspace of a polydisk $(D^2)^m$, where $m$ is the number of vertices in $K$ and $D^2$ is the unit disk of the complex numbers $\\C$, and the natural action of a torus $(S^1)^m$ on $(D^2)^m$ leaves $\\mathcal{Z}_K$ invariant. The Buchstaber invariant $s(K)$ of $K$ is the maximum integer for which there is a subtorus of rank $s(K)$ acting on $\\mathcal{Z}_K$ freely. The story above goes over the real numbers $\\R$ in place of $\\C$ and a real analogue of the Buchstaber invariant, denoted $s_\\R(K)$, can be defined for $K$ and $s(K)\\leqq s_\\R(K)$. In this paper we will make some computations of $s_\\R(K)$ when $K$ is a skeleton of a simplex. We take two approaches to find $s_\\R(K)$ and the latter one turns out to be a problem of integer linear programming and of independent interest.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-09T08:43:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M99",
      "90C05"
    ],
    "keywords": [
      "buchstaber invariant",
      "finite simplicial complex",
      "unit disk",
      "complex numbers",
      "natural action"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.3448F"
    }
  }
}