{
  "id": "math/0111203",
  "version": "v1",
  "published": "2001-11-19T07:02:40.000Z",
  "updated": "2001-11-19T07:02:40.000Z",
  "title": "Linking numbers in rational homology 3-spheres, cyclic branched covers and infinite cyclic covers",
  "authors": [
    "Jozef H. Przytycki",
    "Akira Yasuhara"
  ],
  "comment": "LaTeX, 24 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in $\\Bbb Q$ and in ${Q}({\\Bbb Z}[t,t^{-1}])$ respectively, where ${Q}({\\Bbb Z}[t,t^{-1}])$ denotes the quotient field of ${\\Bbb Z}[t,t^{-1}]$. It is known that the modulo-$\\Bbb Z$ linking number in the rational homology 3-sphere is determined by the linking matrix of the framed link and that the modulo-${\\Bbb Z}[t,t^{-1}]$ linking number in the infinite cyclic cover of the complement of a knot is determined by the Seifert matrix of the knot. We eliminate ` modulo $\\Bbb Z$' and ` modulo ${\\Bbb Z}[t,t^{-1}]$'. When the finite cyclic cover of the 3-sphere branched over a knot is a rational homology 3-sphere, the linking number of a pair in the preimage of a link in the 3-sphere is determined by the Goeritz/Seifert matrix of the knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-11-19T07:02:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M10"
    ],
    "keywords": [
      "infinite cyclic cover",
      "linking number",
      "rational homology",
      "cyclic branched covers",
      "complement"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....11203P"
    }
  }
}