{
  "id": "1502.04436",
  "version": "v1",
  "published": "2015-02-16T06:36:48.000Z",
  "updated": "2015-02-16T06:36:48.000Z",
  "title": "2-torsion in the grope and solvable filtrations of knots",
  "authors": [
    "Hye Jin Jang"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We study knots of order 2 in the grope filtration $\\{\\G_h\\}$ and the solvable filtration $\\{\\F_h\\}$ of the knot concordance group. We show that, for any integer $n\\ge4$, there are knots generating a $\\Z_2^\\infty$ subgroup of $\\G_n/\\G_{n.5}$. Considering the solvable filtration, our knots generate a $\\Z_2^\\infty$ subgroup of $\\F_n/\\F_{n.5}$ $(n\\ge2)$ distinct from the subgroup generated by the previously known 2-torsion knots of Cochran, Harvey, and Leidy. We also present a result on the 2-torsion part in the Cochran, Harvey, and Leidy's primary decomposition of the solvable filtration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-16T06:36:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M25",
      "57N70"
    ],
    "keywords": [
      "solvable filtration",
      "knot concordance group",
      "leidys primary decomposition",
      "study knots",
      "grope filtration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}