{
  "id": "2002.04103",
  "version": "v1",
  "published": "2020-02-10T21:54:07.000Z",
  "updated": "2020-02-10T21:54:07.000Z",
  "title": "$\\operatorname{SL}(2,\\mathbb{C})$ Floer Homology for surgeries on some knots",
  "authors": [
    "Ikshu Neithalath"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We establish a relationship between the sheaf-theoretic $\\operatorname{SL}(2,\\mathbb{C})$ Floer cohomology $\\mathit{HP}(Y)$, as defined by Abouzaid and Manolescu, for $Y$ a surgery on a small knot in $S^3$, and the $\\operatorname{SL}(2,\\mathbb{C})$ Casson invariant, as defined by Curtis. We use this to compute $\\mathit{HP}$ for surgeries on the trefoil and the figure-eight knots. We also compute $\\mathit{HP}$ for surgeries on two non-small knots, the granny and square knots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-10T21:54:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "floer homology",
      "casson invariant",
      "non-small knots",
      "figure-eight knots",
      "floer cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}