{
  "id": "math/9701211",
  "version": "v1",
  "published": "1997-01-24T00:00:00.000Z",
  "updated": "1997-01-24T00:00:00.000Z",
  "title": "Floer homology of Brieskorn homology spheres: solution to Atiyah's problem",
  "authors": [
    "Nikolai Saveliev"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we answer the question posed by M.~Atiyah and give an explicit formula for Floer homology of Brieskorn homology spheres in terms of their branching sets over the 3--sphere. We further show how Floer homology is related to other invariants of knots and 3--manifolds, among which are the $\\bar\\mu$--invariant of W.~Neumann and L.~Siebenmann and the Jones polynomial. Essential progress is made in proving the homology cobordism invariance of our own $\\nu$--invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-01-24T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brieskorn homology spheres",
      "floer homology",
      "atiyahs problem",
      "homology cobordism invariance",
      "jones polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math......1211S"
    }
  }
}