{
  "id": "1501.03222",
  "version": "v1",
  "published": "2015-01-14T00:41:46.000Z",
  "updated": "2015-01-14T00:41:46.000Z",
  "title": "Independence of Satellites of Torus Knots in the Smooth Concordance Group",
  "authors": [
    "Juanita Pinzón-Caicedo"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "The main goal of this article is to obtain a condition under which an infinite collection $\\mathscr{F}$ of satellite knots (with companion a positive torus knot and pattern similar to the Whitehead link) freely generates a subgroup of infinite rank in the smooth concordance group. This goal is attained by examining both the instanton moduli space over a 4-manifold with tubular ends and the corresponding Chern-Simons invariant of the adequate 3-dimensional portion of the 4-manifold. More specifically, the result is derived from Furuta's criterion for the independence of Seifert fibred homology spheres in the homology cobordism group of oriented homology 3-spheres. Indeed, we first associate to $\\mathscr{F}$ the corresponding collection of 2-fold covers of the 3-sphere branched over the elements of $\\mathscr{F}$ and then introduce definite cobordisms from the aforementioned covers of the satellites to a number of Seifert fibered homology spheres. This allows us to apply Furuta's criterion and thus obtain a condition that guarantees the independence of the family $\\mathscr{F}$ in the smooth concordance group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-14T00:41:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N70",
      "58J28"
    ],
    "keywords": [
      "smooth concordance group",
      "torus knot",
      "independence",
      "furutas criterion",
      "instanton moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1342566
    }
  }
}