{
  "id": "math/0510204",
  "version": "v2",
  "published": "2005-10-10T20:10:23.000Z",
  "updated": "2005-10-11T23:32:09.000Z",
  "title": "Combinatorial groupoids, cubical complexes, and the Lovasz conjecture",
  "authors": [
    "Rade T. Zivaljevic"
  ],
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. A new, holonomy-type invariant for cubical complexes is introduced, leading to a combinatorial ``Theorema Egregium'' for cubical complexes non-embeddable into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool for extending Babson-Kozlov-Lovasz graph coloring results to more general statements about non-degenerate maps (colorings) of simplicial complexes and graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-11T23:32:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20L05",
      "05C15",
      "57M15"
    ],
    "keywords": [
      "cubical complexes",
      "combinatorial groupoids",
      "lovasz conjecture",
      "parallel transport",
      "extending babson-kozlov-lovasz graph coloring results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10204Z"
    }
  }
}