{
  "id": "1208.1994",
  "version": "v2",
  "published": "2012-08-09T18:37:10.000Z",
  "updated": "2012-09-10T00:55:55.000Z",
  "title": "A non-abelian analogue of Whitney's 2-isomorphism theorem",
  "authors": [
    "Eric Katz"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a non-abelian analogue of Whitney's 2-isomorphism theorem for graphs. Whitney's theorem states that the cycle space determines a graph up to 2-isomorphism. Instead of considering the cycle space of a graph which is an abelian object, we consider a mildly non-abelian object, the 2-truncation of the group algebra of the fundamental group of the graph considered as a subalgebra of the 2-truncation of the group algebra of the free group on the edges. The analogue of Whitney's theorem is that this is a complete invariant of 2-edge connected graphs: let G,G' be 2-edge connected finite graphs; if there is a bijective correspondence between the edges of G and G' that induces equality on the 2-truncations of the group algebras of the fundamental groups, then G and G' are isomorphic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-10T00:55:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-abelian analogue",
      "group algebra",
      "fundamental group",
      "whitneys theorem states",
      "cycle space determines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1994K"
    }
  }
}