{
  "id": "1711.05991",
  "version": "v1",
  "published": "2017-11-16T09:05:39.000Z",
  "updated": "2017-11-16T09:05:39.000Z",
  "title": "On the stable Andreadakis problem",
  "authors": [
    "Jacques Darné"
  ],
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "Let $F\\_n$ be the free group on $n$ generators. Consider the group $IA\\_n$ of automorpisms of $F\\_n$ acting trivially on its abelianization. There are two canonical filtrations on $IA\\_n$: the first one is its lower central series $\\Gamma\\_*$; the second one is the Andreadakis filtration $\\mathcal A\\_*$, defined from the action on $F\\_n$. In this paper, we establish that the canonical morphism between the associated graded Lie rings ${\\mathcal L}(\\Gamma\\_*)$ and ${\\mathcal L}(\\mathcal A\\_*)$ is stably surjective. We then investigate a $p$-restricted version of the Andreadakis problem. A calculation of the Lie algebra of the classical congruence group is also included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-16T09:05:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable andreadakis problem",
      "lower central series",
      "andreadakis filtration",
      "lie algebra",
      "associated graded lie rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}