{
  "id": "math/0610501",
  "version": "v6",
  "published": "2006-10-16T23:54:13.000Z",
  "updated": "2008-06-06T23:36:30.000Z",
  "title": "Intrinsic linking and knotting are arbitrarily complex",
  "authors": [
    "Erica Flapan",
    "Blake Mellor",
    "Ramin Naimi"
  ],
  "comment": "18 pages, 5 figures. Proposition 2 has been strengthened, and Corollary 1 and Proposition 3 have been added to answer a question of Taniyama's",
  "journal": "Fund. Math., vol. 201, no. 2, 2008, pp. 131-148",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We show that, given any $n$ and $\\alpha$, every embedding of any sufficiently large complete graph in $\\mathbb{R}^3$ contains an oriented link with components $Q_1$, ..., $Q_n$ such that for every $i\\not =j$, $|\\lk(Q_i,Q_j)|\\geq\\alpha$ and $|a_2(Q_i)|\\geq\\alpha$, where $a_{2}(Q_i)$ denotes the second coefficient of the Conway polynomial of $Q_i$.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2008-06-06T23:36:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M15",
      "05C10"
    ],
    "keywords": [
      "arbitrarily complex",
      "intrinsic linking",
      "sufficiently large complete graph",
      "second coefficient",
      "conway polynomial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10501F"
    }
  }
}