{
  "id": "2103.15277",
  "version": "v1",
  "published": "2021-03-29T02:02:59.000Z",
  "updated": "2021-03-29T02:02:59.000Z",
  "title": "Applications of the Casson-Walker invariant to the knot complement and the cosmetic crossing conjectures",
  "authors": [
    "Tetsuya Ito"
  ],
  "comment": "14 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a rational surgery formula for the Casson-Walker invariant of a 2-component link in $S^{3}$ which is a generalization of Matveev-Polyak's formula. As application, we give more examples of non-hyperbolic L-space $M$ such that knots in $M$ are determined by their complements. We also apply the result for the cosmetic crossing conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-29T02:02:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cosmetic crossing conjecture",
      "casson-walker invariant",
      "knot complement",
      "application",
      "rational surgery formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}