{
  "id": "math/0203042",
  "version": "v1",
  "published": "2002-03-05T14:14:01.000Z",
  "updated": "2002-03-05T14:14:01.000Z",
  "title": "A norm for the cohomology of 2-complexes",
  "authors": [
    "Vladimir Turaev"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-7.abs.html",
  "journal": "Algebr. Geom. Topol. 2 (2002) 137-155",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We introduce a norm on the real 1-cohomology of finite 2-complexes determined by the Euler characteristics of graphs on these complexes. We also introduce twisted Alexander-Fox polynomials of groups and show that they give rise to norms on the real 1-cohomology of groups. Our main theorem states that for a finite 2-complex X, the norm on H^1(X; R) determined by graphs on X majorates the Alexander-Fox norms derived from \\pi_1(X).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-05T14:14:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M20",
      "57M05"
    ],
    "keywords": [
      "cohomology",
      "main theorem states",
      "euler characteristics",
      "twisted alexander-fox polynomials",
      "alexander-fox norms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}