{
  "id": "2505.03928",
  "version": "v1",
  "published": "2025-05-06T19:08:05.000Z",
  "updated": "2025-05-06T19:08:05.000Z",
  "title": "Torus decomposition and foliation detected slopes",
  "authors": [
    "Qingfeng Lyu"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $M_1$ and $M_2$ be knot manifolds and $M=M_1\\cup_f M_2$ be the closed 3-manifold obtained by gluing up $M_1$ and $M_2$ via $f:\\partial M_1\\xrightarrow{\\cong} \\partial M_2$. We show that if $M$ admits a co-oriented taut foliation, then $f$ identifies some CTF-detected rational boundary slopes of $M_1$ and $M_2$, affirming a conjecture proposed by Boyer, Gordon and Hu.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-06T19:08:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K30",
      "57R30"
    ],
    "keywords": [
      "foliation detected slopes",
      "torus decomposition",
      "ctf-detected rational boundary slopes",
      "co-oriented taut foliation",
      "knot manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}