{
  "id": "1809.10588",
  "version": "v1",
  "published": "2018-09-27T15:53:14.000Z",
  "updated": "2018-09-27T15:53:14.000Z",
  "title": "Property testing and expansion in cubical complexes",
  "authors": [
    "David Garber",
    "Uzi Vishne"
  ],
  "comment": "22 pages; submitted to publication",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider expansion and property testing in the language of incidence geometry, covering both simplicial and cubical complexes in any dimension. We develop a general method for passing from an explicit description of the cohomology group, which need not be trivial, to a testability proof. The method is demonstrated by testing functions on $2$-cells in cubical complexes to be induced from the edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-27T15:53:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "15U10",
      "18G35"
    ],
    "keywords": [
      "cubical complexes",
      "property testing",
      "testability proof",
      "cohomology group",
      "incidence geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}