{
  "id": "2304.09312",
  "version": "v1",
  "published": "2023-04-18T21:50:34.000Z",
  "updated": "2023-04-18T21:50:34.000Z",
  "title": "A bound on the number of twice-punctured tori in a knot exterior",
  "authors": [
    "Román Aranda",
    "Enrique Ramírez-Losada",
    "Jesús Rodríguez-Viorato"
  ],
  "comment": "15 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "This paper continues a program due to Motegi regarding universal bounds for the number of non-isotopic essential $n$-punctured tori in the complement of a hyperbolic knot in $S^3$. For $n=1$, Valdez-S\\'anchez showed that there are at most five non-isotopic Seifert tori in the exterior of a hyperbolic knot. In this paper, we address the case $n=2$. We show that there are at most six non-isotopic, nested, essential 2-holed tori in the complement of every hyperbolic knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-18T21:50:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "knot exterior",
      "twice-punctured tori",
      "hyperbolic knot",
      "motegi regarding universal bounds",
      "non-isotopic seifert tori"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}