{
  "id": "0705.2874",
  "version": "v1",
  "published": "2007-05-21T12:07:51.000Z",
  "updated": "2007-05-21T12:07:51.000Z",
  "title": "Combinatorial Morse theory and minimality of hyperplane arrangements",
  "authors": [
    "Mario Salvetti",
    "Simona Settepanella"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "We find an explicit combinatorial gradient vector field on the well known complex S (Salvetti complex) which models the complement to an arrangement of complexified hyperplanes. The argument uses a total ordering on the facets of the stratification of R^n associated to the arrangement, which is induced by a generic system of polar coordinates. We give a combinatorial description of the singular facets, finding also an algebraic complex which computes local homology. We also give a precise construction in the case of the braid arrangement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-21T12:07:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35",
      "32S22"
    ],
    "keywords": [
      "combinatorial morse theory",
      "hyperplane arrangements",
      "explicit combinatorial gradient vector field",
      "minimality",
      "local homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.2874S"
    }
  }
}