{
  "id": "1211.0078",
  "version": "v5",
  "published": "2012-11-01T02:56:13.000Z",
  "updated": "2013-11-19T18:38:07.000Z",
  "title": "Full-featured peak reduction in right-angled Artin groups",
  "authors": [
    "Matthew B. Day"
  ],
  "comment": "72 pages, 1 figure. Updated to incorporate referee comments",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove a new version of the classical peak-reduction theorem for automorphisms of free groups in the setting of right-angled Artin groups. We use this peak-reduction theorem to prove two important corollaries about the action of the automorphism group of a right-angled Artin group $A_\\Gamma$ on the set of $k$-tuples of conjugacy classes from $A_\\Gamma$: orbit membership is decidable, and stabilizers are finitely presentable. Further, we explain procedures for checking orbit membership and building presentations of stabilizers. This improves on a previous result of the author's. We overcome a technical difficulty from the previous work by considering infinite generating sets for the automorphism groups. The method also involves a variation on the Hermite normal form for matrices.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-11-19T18:38:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F28"
    ],
    "keywords": [
      "right-angled artin group",
      "full-featured peak reduction",
      "automorphism group",
      "hermite normal form",
      "important corollaries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 72,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.0078D"
    }
  }
}