{
  "id": "2010.13169",
  "version": "v1",
  "published": "2020-10-25T17:32:54.000Z",
  "updated": "2020-10-25T17:32:54.000Z",
  "title": "Spaces of Pants Decompositions for Surfaces of Infinite Type",
  "authors": [
    "B. Branman"
  ],
  "comment": "34 pages, 4 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We study the pants complex of surfaces of infinite type. When $S$ is a surface of infinite type, the usual definition of the pants graph $\\mathcal{P}(S)$ yields a graph with infinitely many connected-components. In the first part of our paper, we study this disconnected graph. In particular, we show that the extended mapping class group $\\mathrm{Mod}(S)$ is isomorphic to a proper subgroup of $\\mathrm{Aut}(\\mathcal{P})$, in contrast to the finite-type case where $\\mathrm{Mod}(S)\\cong \\mathrm{Aut}(\\mathcal{P}(S))$. In the second part of the paper, motivated by the Metaconjecture of Ivanov \\cite{IvanovMeta}, we seek to endow $\\mathcal{P}(S)$ with additional structure. To this end, we define a coarser topology on $\\mathcal{P}(S)$ than the topology inherited from the graph structure. We show that our new space is path-connected, and that its automorphism group is isomorphic to $\\mathrm{Mod}(S)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-25T17:32:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M07",
      "37E30"
    ],
    "keywords": [
      "infinite type",
      "pants decompositions",
      "graph structure",
      "usual definition",
      "pants graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}