{
  "annotation_id": "2053fa45-2674-4320-8360-f4313287c086",
  "date_created": "2026-02-17T05:53:08.822000Z",
  "date_modified": "2026-02-17T05:53:08.822000Z",
  "file_hash": "d68deeae10c712474c01ea4559515de03efe2edc1d701bc31592ac21d30c3772",
  "private": false,
  "record": {
    "abstract": "We construct a new family of surgery exact triangles in Heegaard Floer theory over the field with two elements. This family generalizes both Ozsv\\\u0027{a}th and Szab\\\u0027{o}\u0027s $n$- and $1/n$-surgery exact triangles for positive integers $n$ and the author\u0027s recent 2-surgery exact triangle to all positive rational slopes.\n  The construction reduces to a combinatorial problem that involves triangle and quadrilateral counting maps in a genus 1 Heegaard diagram. The main contribution of this paper is solving this combinatorial problem, which is particularly tricky for slopes $r\\neq n,1/n$; one key idea is to use an involution that is closely related to the ${\\rm Spin}^{c}$ conjugation symmetry.",
    "arxiv_id": "2601.06654",
    "authors": [
      "Gheehyun Nahm"
    ],
    "categories": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Rational surgery exact triangles in Heegaard Floer homology",
    "url": "https://arxiv.org/abs/2601.06654",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6445e269-80bd-4bee-af11-9d3549e3ad11",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}