{
  "id": "1307.7098",
  "version": "v2",
  "published": "2013-07-26T16:59:56.000Z",
  "updated": "2013-08-12T16:38:08.000Z",
  "title": "$\\mathfrak{S}$-coalgebras determine fundamental groups",
  "authors": [
    "Justin R. Smith"
  ],
  "comment": "17 pages. arXiv admin note: text overlap with arXiv:1304.6328",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper, we extend earlier work by showing that if $X$ and $Y$ are simplicial complexes (i.e. simplicial sets whose nondegenerate simplices are determined by their vertices), an isomorphism $\\mathcal{C}(X)\\cong\\mathcal{C}(Y)$ of coalgebras over the Barratt-Eccles operad implies that the 3-skeleton of $X$ is weakly equivalent to the 3-skeleton of $Y$, also implying that $\\pi_{1}(X)=\\pi_{1}(Y)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-12T16:38:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G55",
      "55U40"
    ],
    "keywords": [
      "coalgebras determine fundamental groups",
      "barratt-eccles operad implies",
      "extend earlier work",
      "nondegenerate simplices",
      "simplicial complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7098S"
    }
  }
}