{
  "id": "0909.4825",
  "version": "v1",
  "published": "2009-09-26T01:46:16.000Z",
  "updated": "2009-09-26T01:46:16.000Z",
  "title": "Infinite generation of the kernels of the Magnus and Burau representations",
  "authors": [
    "Thomas Church",
    "Benson Farb"
  ],
  "comment": "13 pages, 7 figures",
  "journal": "Algebraic and Geometric Topology 10 (2010), 837-851",
  "doi": "10.2140/agt.2010.10.837",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Consider the kernel Mag_g of the Magnus representation of the Torelli group and the kernel Bur_n of the Burau representation of the braid group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and Bur_n have infinite rank first homology. As a consequence we conclude that neither group has any finite generating set. The method of proof in each case consists of producing a kind of \"Johnson-type\" homomorphism to an infinite rank abelian group, and proving the image has infinite rank. For the case of Bur_n, we do this with the assistance of a computer calculation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-26T01:46:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "burau representation",
      "infinite generation",
      "infinite rank abelian group",
      "infinite rank first homology",
      "braid group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4825C"
    }
  }
}