{
  "annotation_id": "14debbc5-7d3a-421d-a5bb-234d96fce9f8",
  "date_created": "2026-03-02T18:01:27.607000Z",
  "date_modified": "2026-03-02T18:01:27.607000Z",
  "file_hash": "7674ffd5df3428b467f463bef976c4d2551d7b0f8625dd6d5c22ad3beea03f47",
  "private": false,
  "record": {
    "abstract": "A. Casson defined an intersection number invariant which can be roughly\nthought of as the number of conjugacy classes of irreducible representations of\n$\\pi_1(Y)$ into $SU(2)$ counted with signs, where $Y$ is an oriented integral\nhomology 3-sphere. X.S. Lin defined an similar invariant (signature of a knot)\nto a braid representative of a knot in $S^3$. In this paper, we give a natural\ngeneralization of the Casson-Lin\u0027s invariant to be (instead of using the\ninstanton Floer homology) the symplectic Floer homology for the representation\nspace (one singular point) of $\\pi_1(S^3 \\setminus K)$ into $SU(2)$ with\ntrace-free along all meridians. The symplectic Floer homology of braids is a\nnew invariant of knots and its Euler number of such a symplectic Floer homology\nis the negative of the Casson-Lin\u0027s invariant.",
    "arxiv_id": "q-alg/9605036",
    "authors": [
      "Weiping Li"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Casson-Lin\u0027s invariant of a knot and Floer homology",
    "url": "https://arxiv.org/abs/q-alg/9605036"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "392c9777-a17e-446e-a50d-12531670a68c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}