{
  "id": "math/0411570",
  "version": "v2",
  "published": "2004-11-25T10:46:54.000Z",
  "updated": "2007-10-17T11:42:24.000Z",
  "title": "Enriched homology and cohomology modules of simplicial complexes",
  "authors": [
    "Gunnar Floystad"
  ],
  "comment": "22 pages, some new material on designs",
  "journal": "J. Algebraic Combinatorics 25 (2007), no. 3, p. 285-307",
  "doi": "10.1007/s10801-006-0038-z",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "For a simplicial complex X on {1,2, ..., n} we define enriched homology and cohomology modules. They are graded modules over k[x_1, ..., x_n] whose ranks are equal to the dimensions of the reduced homology and cohomology groups. We characterize Cohen-Macaulay, l-Cohen-Macaulay, Buchsbaum, and Gorenstein* complexes X, and also orientable manifolds in terms of the enriched modules. We introduce the notion of girth for simplicial complexes and make a conjecture relating the girth to invariants of the simplicial complex. We also put strong vanishing conditions on the enriched homology modules and describe the simplicial complexes we then get. They are block designs and include Steiner systems S(c,d,n) and cyclic polytopes of even dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-10-17T11:42:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F55",
      "55U10",
      "13D99"
    ],
    "keywords": [
      "simplicial complexes",
      "cohomology modules",
      "cyclic polytopes",
      "define enriched homology",
      "steiner systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11570F"
    }
  }
}