{
  "id": "1209.3476",
  "version": "v1",
  "published": "2012-09-16T11:47:27.000Z",
  "updated": "2012-09-16T11:47:27.000Z",
  "title": "On the number of connected components in complements to arrangements of submanifolds",
  "authors": [
    "I. N. Shnurnikov"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We consider arrangements of n connected codimensional one submanifolds in closed d-dimensional manifold M. Let f be the number of connected components of the complement in M to the union of submanifolds. We prove the sharp lower bound for f via n and homology group H_{d-1}(M). The sets of all possible f-values for given n are studied for hyperplane arrangements in real projective spaces and for subtori arrangements in d-dimensional tori.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-16T11:47:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35"
    ],
    "keywords": [
      "connected components",
      "submanifolds",
      "complement",
      "sharp lower bound",
      "d-dimensional tori"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3476S"
    }
  }
}