{
  "id": "2308.15569",
  "version": "v1",
  "published": "2023-08-29T18:49:20.000Z",
  "updated": "2023-08-29T18:49:20.000Z",
  "title": "On lens space surgeries from the Poincaré homology sphere",
  "authors": [
    "Jacob Caudell"
  ],
  "comment": "66 pages. Comments welcome!",
  "categories": [
    "math.GT"
  ],
  "abstract": "Building on Greene's changemaker lattices, we develop a lattice embedding obstruction to realizing an L-space bounding a definite 4-manifold as integer surgery on a knot in the Poincar\\'e homology sphere. As the motivating application, we determine which lens spaces are realized by $p/q$-surgery on a knot $K$ when $p/q > 2g(K) -1$. Specifically, we use the lattice embedding obstruction to show that if $K(p)$ is a lens space and $p \\geq 2g(K)$, then there exists an equivalent surgery on a Tange knot with the same knot Floer homology groups; additionally, using input from Baker, Hedden, and Ni, we identify the only two knots in the Poincar\\'e homology sphere that admit half-integer lens space surgeries. Thus, together with the Finite/Cyclic Surgery Theorem of Boyer and Zhang, we obtain the corollary that lens space surgeries on hyperbolic knots in the Poincar\\'e homology sphere are integral.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-29T18:49:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10"
    ],
    "keywords": [
      "poincare homology sphere",
      "lattice embedding obstruction",
      "admit half-integer lens space surgeries",
      "knot floer homology groups",
      "greenes changemaker lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}