{
  "id": "2209.13124",
  "version": "v1",
  "published": "2022-09-27T02:47:29.000Z",
  "updated": "2022-09-27T02:47:29.000Z",
  "title": "Morse-Novikov numbers, tunnel numbers, and handle numbers of sutured manifolds",
  "authors": [
    "Kenneth L. Baker",
    "Fabiola Manjarrez-Gutiérrez"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "Developed from geometric arguments for bounding the Morse-Novikov number of a link in terms of its tunnel number, we obtain upper and lower bounds on the handle number of a Heegaard splitting of a sutured manifold $(M,\\gamma)$ in terms of the handle number of its decompositions along a surface representing a given 2nd homology class. Fixing the sutured structure $(M,\\gamma)$, this leads us to develop the handle number function $h \\colon H_2(M,\\partial M;\\mathbb{R}) \\to \\mathbb{N}$ which is bounded, constant on rays from the origin, and locally maximal. Furthermore, for an integral class $\\xi$, $h(\\xi)=0$ if and only if the decomposition of $(M,\\gamma)$ along some surface representing $\\xi$ is a product manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-27T02:47:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K35",
      "57K99"
    ],
    "keywords": [
      "morse-novikov number",
      "tunnel number",
      "sutured manifold",
      "2nd homology class",
      "handle number function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}