{
  "id": "math/0702608",
  "version": "v1",
  "published": "2007-02-21T09:39:56.000Z",
  "updated": "2007-02-21T09:39:56.000Z",
  "title": "Pseudo-Anosov homeomorphisms and the lower central series of a surface group",
  "authors": [
    "Justin Malestein"
  ],
  "comment": "23 pages, 8 figures; previous versions of this paper had the title: An algebraic criterion to detect pseudo-Anosovs",
  "journal": "Algebr. Geom. Topol. {\\bf 7} (2007), pp. 1921--1948",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let Gamma_k be the lower central series of a surface group Gamma of a compact surface S with one boundary component. A simple question to ponder is whether a mapping class of S can be determined to be pseudo-Anosov given only the data of its action on Gamma/Gamma_k for some k. In this paper, to each mapping class f which acts trivially on Gamma/Gamma_{k+1}, we associate an invariant Psi_k(f) in End(H_1(S, Z)) which is constructed from its action on Gamma/Gamma_{k+2} . We show that if the characteristic polynomial of Psi_k(f) is irreducible over Z, then f must be pseudo-Anosov. Some explicit mapping classes are then shown to be pseudo-Anosov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-21T09:39:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60",
      "37E30"
    ],
    "keywords": [
      "lower central series",
      "pseudo-anosov homeomorphisms",
      "surface group gamma",
      "boundary component",
      "compact surface"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2608M"
    }
  }
}