{
  "id": "1505.04993",
  "version": "v1",
  "published": "2015-05-19T13:45:34.000Z",
  "updated": "2015-05-19T13:45:34.000Z",
  "title": "Connected primitive disk complexes and genus two Goeritz groups of lens spaces",
  "authors": [
    "Sangbum Cho",
    "Yuya Koda"
  ],
  "comment": "32 pages, 17 figures; This is an extended version of our earlier preprint arXiv:1206.6243 \"Primitive disk complexes for lens spaces\", which deals with the structure of the primitive disk complexes for lens spaces. The arguments are polished under a new organization, and further a new application is combined",
  "categories": [
    "math.GT"
  ],
  "abstract": "Given a stabilized Heegaard splitting of a $3$-manifold, the primitive disk complex for the splitting is the subcomplex of the disk complex for a handlebody in the splitting spanned by the vertices of the primitive disks. In this work, we study the structure of the primitive disk complex for the genus two Heegaard splitting of each lens space. In particular, we show that the complex for the genus two splitting for the lens space $L(p, q)$ with $1\\leq q \\leq p/2$ is connected if and only if $p \\equiv \\pm 1 \\pmod q$, and describe the combinatorial structure of each of those complexes. As an application, we obtain a finite presentation of the genus two Goeritz group of each of those lens spaces, the group of isotopy classes of orientation preserving homeomorphisms of the lens space that preserve the genus two Heegaard splitting of it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T13:45:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M60"
    ],
    "keywords": [
      "lens space",
      "connected primitive disk complexes",
      "goeritz group",
      "heegaard splitting",
      "finite presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504993C"
    }
  }
}