{
  "id": "2104.09253",
  "version": "v1",
  "published": "2021-04-19T12:50:54.000Z",
  "updated": "2021-04-19T12:50:54.000Z",
  "title": "Mapping class group actions on configuration spaces and the Johnson filtration",
  "authors": [
    "Andrea Bianchi",
    "Jeremy Miller",
    "Jennifer C. H. Wilson"
  ],
  "comment": "28 pages, 14 figures",
  "categories": [
    "math.GT",
    "math.AT",
    "math.GN"
  ],
  "abstract": "Let $F_n(\\Sigma_{g,1})$ denote the configuration space of $n$ ordered points on the surface $\\Sigma_{g,1}$ and let $\\Gamma_{g,1}$ denote the mapping class group of $\\Sigma_{g,1}$. We prove that the action of $\\Gamma_{g,1}$ on $H_i(F_n(\\Sigma_{g,1});\\mathbb{Z})$ is trivial when restricted to the $i^{th}$ stage of the Johnson filtration $\\mathcal{J}(i)\\subset \\Gamma_{g,1}$. We give examples showing that $\\mathcal{J}(2)$ acts nontrivially on $H_3(F_3(\\Sigma_{g,1}))$ for $g\\ge 2$, and provide two new conceptual reinterpretations of a certain group introduced by Moriyama.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-19T12:50:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "57K20"
    ],
    "keywords": [
      "mapping class group actions",
      "configuration space",
      "johnson filtration",
      "conceptual reinterpretations",
      "ordered points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}