{
  "id": "math/9904100",
  "version": "v2",
  "published": "1999-04-20T15:32:07.000Z",
  "updated": "1999-11-30T00:00:00.000Z",
  "title": "The Burau representation is not faithful for n = 5",
  "authors": [
    "Stephen Bigelow"
  ],
  "comment": "8 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper16.abs.html",
  "journal": "Geom. Topol. 3 (1999), 397-404",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "The Burau representation is a natural action of the braid group B_n on the free Z[t,t^{-1}]-module of rank n-1. It is a longstanding open problem to determine for which values of n this representation is faithful. It is known to be faithful for n=3. Moody has shown that it is not faithful for n>8 and Long and Paton improved on Moody's techniques to bring this down to n>5. Their construction uses a simple closed curve on the 6-punctured disc with certain homological properties. In this paper we give such a curve on the 5-punctured disc, thus proving that the Burau representation is not faithful for n>4.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-11-30T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "57M07",
      "20C99"
    ],
    "keywords": [
      "burau representation",
      "braid group",
      "longstanding open problem",
      "natural action",
      "moodys techniques"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}