{
  "id": "1211.2144",
  "version": "v3",
  "published": "2012-11-09T14:28:45.000Z",
  "updated": "2019-03-04T06:35:28.000Z",
  "title": "The classifying space of the $G$-cobordism category in dimension two",
  "authors": [
    "Carlos Segovia"
  ],
  "comment": "20 pages, 7 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "For $G$ a finite group, we define the $G$-cobordism category in dimension two. We prove this category has connected components in bijection with the abelianization of $G$ and with fundamental group isomorphic to a lattice. The main result consists of an splitting of the classifying space of the $G$-cobordism category as the product of the abelianization of $G$, an infinite loop space and a finite product of circles. In addition, we study the classifying space of some important subcategories.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-29T09:16:27.000Z",
      "title": "The classifying space of the 1+1 dimensional G-cobordism category",
      "abstract": "The 1+1 G-cobordism category, with G a finite group, is important in the construction of G-topological field theories which are completely determined by a G-Frobenius algebra. We give a description of the classifying space of this category generalizing the work of Ulrike Tillmann. Moreover, we compute the connected components and the fundamental group of this classifying space and we give a complete description of the classifying spaces of some important subcategories. Finally, we present some relations between the rank of the fundamental group of the G-cobordism category and the number of subgroups of the group G.",
      "comment": "21 pages, 25 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2019-03-04T06:35:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R85",
      "55P91"
    ],
    "keywords": [
      "classifying space",
      "dimensional g-cobordism category",
      "fundamental group",
      "g-topological field theories",
      "important subcategories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2144S"
    }
  }
}