{
  "id": "math/0011163",
  "version": "v1",
  "published": "2000-11-21T19:43:25.000Z",
  "updated": "2000-11-21T19:43:25.000Z",
  "title": "n-dimensional links, their components, and their band-sums",
  "authors": [
    "Eiji Ogasa"
  ],
  "comment": "16 pages, no figure",
  "categories": [
    "math.GT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove the following results (1) (2) (3) on relations between $n$-links and their components. (1) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\\geq 5). Then we have Arf L=Arf L_1+Arf L_2. (2) Let L=(L_1, L_2) be a (4k+3)-link (4k+3\\geq3). Then we have \\sigma L=\\sigma L_1+\\sigma L_2. (3) Let n\\geq1. Then there is a nonribbon n-link L=(L_1, L_2) such that L_i is a trivial knot. We prove the following results (4) (5) (6) (7) on band-sums of n-links. (4) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\\geq 5). Let K be a band-sum of L. Then we have Arf K=Arf L_1+Arf L_2. (5) Let L=(L_1, L_2) be a (4k+3)-link (4k+3\\geq3). Let K be a band-sum of L. Then we have \\sigma K=\\sigma L_1+ \\sigma L_2. The above (4)(5) imply the following (6). (6) Let 2m+1\\geq3. There is a set of three (2m+1)-knots K_0, K_1, K_2 with the following property: K_0 is not any band-sum of any n-link L=(L_1, L_2) such that L_i is equivalent to K_i (i=1,2). (7) Let n\\geq1. Then there is an n-link L=(L_1, L_2) such that L_i is a trivial knot (i=1,2) and that a band-sum of $L$ is a nonribbon knot. We prove a 1-dimensional version of (1). (8) Let L=(L_1, L_2) be a proper 1-link. Then Arf L =Arf L_1+ Arf L_2+{1/2}\\{\\beta^*(L)$+mod4 $\\{{1/2}lk (L)\\}\\} =Arf L_1+Arf L_2+mod2 \\{\\lambda (L)\\}, where \\beta^*(L) is the Saito-Sato-Levine invariant and \\lambda(L) is the Kirk-Livingston invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-11-21T19:43:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57Q45",
      "57R65"
    ],
    "keywords": [
      "n-dimensional links",
      "components",
      "trivial knot",
      "nonribbon knot",
      "nonribbon n-link"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....11163O"
    }
  }
}