{
  "id": "math/0504206",
  "version": "v3",
  "published": "2005-04-10T22:48:45.000Z",
  "updated": "2008-11-14T09:33:04.000Z",
  "title": "On the homology of the space of knots",
  "authors": [
    "Ryan Budney",
    "Frederick Cohen"
  ],
  "comment": "36 pages, 6 figures. v3: small revisions before publication",
  "journal": "Geometry & Topology 13 (2009) 99--139",
  "categories": [
    "math.GT",
    "math.AT",
    "math.QA"
  ],
  "abstract": "Consider the space of `long knots' in R^n, K_{n,1}. This is the space of knots as studied by V. Vassiliev. Based on previous work of the authors, it follows that the rational homology of K_{3,1} is free Gerstenhaber-Poisson algebra. A partial description of a basis is given here. In addition, the mod-p homology of this space is a `free, restricted Gerstenhaber-Poisson algebra'. Recursive application of this theorem allows us to deduce that there is p-torsion of all orders in the integral homology of K_{3,1}. This leads to some natural questions about the homotopy type of the space of long knots in R^n for n>3, as well as consequences for the space of smooth embeddings of S^1 in S^3.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-11-14T09:33:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D10",
      "57T25",
      "57M25",
      "57Q45"
    ],
    "keywords": [
      "long knots",
      "free gerstenhaber-poisson algebra",
      "rational homology",
      "partial description",
      "mod-p homology"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4206B"
    }
  }
}