{
  "id": "math/0205245",
  "version": "v3",
  "published": "2002-05-23T15:02:01.000Z",
  "updated": "2005-06-16T14:39:33.000Z",
  "title": "Spindle configurations of skew lines",
  "authors": [
    "Roland Bacher",
    "David Garber"
  ],
  "comment": "42 pages, many figures. A new corrected proof of a conjecture of Crapo and Penne is added. More new material is also added",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly simplify the exposition of some known invariants for configurations of skew lines and use them to define a natural partition of the lines in a skew configuration. Finally, we describe an algorithm which constructs a spindle in a given switching class, or proves non-existence of such a spindle.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-16T14:39:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "skew lines",
      "spindle configurations",
      "skew configuration",
      "characterizes isotopy classes",
      "natural partition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5245B"
    }
  }
}