{
  "id": "1701.03490",
  "version": "v1",
  "published": "2017-01-12T20:12:34.000Z",
  "updated": "2017-01-12T20:12:34.000Z",
  "title": "Representation Stability for Configuration Spaces of Graphs",
  "authors": [
    "Daniel Lütgehetmann"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We consider for two based graphs $G$ and $H$ the sequence of graphs $G_k$ given by the wedge sum of $G$ and $k$ copies of $H$. These graphs have an action of the symmetric group $\\Sigma_k$ by permuting the $H$-summands. We show that the sequence of representations of the symmetric group $H_q(\\mathrm{Conf}_n(G_\\bullet); \\mathbf{Q})$, the homology of the ordered configuration space of these spaces, is representation stable in the sense of Church and Farb. In the case where $G$ and $H$ are trees, we provide a similar result for glueing along arbitrary subtrees instead of the base point. Furthermore, we give similar stabilization results for configurations in spaces without any obvious action of the symmetric group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-12T20:12:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "57M15"
    ],
    "keywords": [
      "representation stability",
      "symmetric group",
      "similar stabilization results",
      "wedge sum",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}