{
  "id": "2208.01608",
  "version": "v1",
  "published": "2022-08-02T17:32:25.000Z",
  "updated": "2022-08-02T17:32:25.000Z",
  "title": "Non-trivial action of the Johnson filtration on the homology of configuration spaces",
  "authors": [
    "Andrea Bianchi",
    "Andreas Stavrou"
  ],
  "categories": [
    "math.GT",
    "math.AT",
    "math.GN"
  ],
  "abstract": "We let the mapping class group $\\Gamma_{g,1}$ of a genus $g$ surface $\\Sigma_{g,1}$ with one boundary component act on the homology $H_*(F_{n}(\\Sigma_{g,1});\\mathbb{Q})$ of the $n^{th}$ ordered configuration space of the surface. We prove that the action is non-trivial when restricted to the $(n-1)^{st}$ stage of the Johnson filtration, for all $n\\ge 1$ and $g\\ge 2$. We deduce an analogous result for closed surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-02T17:32:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "57K20"
    ],
    "keywords": [
      "johnson filtration",
      "non-trivial action",
      "boundary component act",
      "ordered configuration space",
      "mapping class group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}