{
  "id": "1008.5089",
  "version": "v2",
  "published": "2010-08-30T14:33:37.000Z",
  "updated": "2011-03-14T13:11:16.000Z",
  "title": "On the homotopy type of certain cobordism categories of surfaces",
  "authors": [
    "George Raptis"
  ],
  "comment": "32 pages, minor changes and corrections, some more details added, submitted version",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "Let $\\mathcal{A}_{g,d}$ be the (topological) cobordism category of orientable surfaces whose connected components are homeomorphic to either $S^1 \\times I$ with one incoming and one outgoing boundary component or the surface $\\Sigma_{g,d}$ of genus $g$ and $d$ boundary components that are all incoming. In this paper, we study the homotopy type of the classifying space of the cobordism categories $\\mathcal{A}_{g,d}$ and the associated (ordinary) cobordism categories of their connected components $\\mathbb{A}_d$. $\\mathcal{A}_{0,2}$ is the cobordism category of complex annuli that was considered by Costello and $\\mathbb{A}_2$ is homotopy equivalent with the positive boundary 1-dimensional embedded cobordism category of Galatius-Madsen-Tillmann-Weiss. We identify their homotopy type with the infinite loop spaces associated with certain Thom spectra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-14T13:11:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy type",
      "connected components",
      "thom spectra",
      "complex annuli",
      "outgoing boundary component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.5089R"
    }
  }
}