{
  "id": "2202.06713",
  "version": "v1",
  "published": "2022-02-14T14:02:15.000Z",
  "updated": "2022-02-14T14:02:15.000Z",
  "title": "Branched covers and rational homology balls",
  "authors": [
    "Charles Livingston"
  ],
  "comment": "5 page, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The concordance group of knots in the three-sphere contains an infinite subgroup generated by elements of order two, each one of which is represented by a knot K with the property that for every n > 0, the n-fold cyclic cover of S^3 branched over K bounds a rational homology ball. This implies that the kernel of the canonical homomorphism from the knot concordance group to the infinite direct sum of rational homology cobordism groups (defined via prime-power branched covers) contains an infinitely generated two-torsion subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-14T14:02:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10"
    ],
    "keywords": [
      "rational homology ball",
      "branched covers",
      "rational homology cobordism groups",
      "n-fold cyclic cover",
      "infinite direct sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}