{
  "id": "math/0702669",
  "version": "v1",
  "published": "2007-02-22T18:07:30.000Z",
  "updated": "2007-02-22T18:07:30.000Z",
  "title": "Cohomology in one-dimensional substitution tiling spaces",
  "authors": [
    "Marcy Barge",
    "Beverly Diamond"
  ],
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which ``forces its border.'' One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is computed as the direct limit of the homomorphism induced by inflation and substitution on the cohomology of the complex. For one-dimensional substitution tiling spaces, we describe a modification of the Anderson-Putnam complex on collared tiles that allows for easier computation and provides a means of identifying certain special features of the tiling space with particular elements of the cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-22T18:07:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "55N05",
      "54H20"
    ],
    "keywords": [
      "one-dimensional substitution tiling spaces",
      "cohomology",
      "collared tiles",
      "direct limit",
      "special features"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2669B"
    }
  }
}