{
  "id": "1904.11730",
  "version": "v1",
  "published": "2019-04-26T09:17:11.000Z",
  "updated": "2019-04-26T09:17:11.000Z",
  "title": "On the Burau representation for $n=4$",
  "authors": [
    "A. Beridze",
    "P. Traczyk"
  ],
  "categories": [
    "math.GT",
    "math.RT"
  ],
  "abstract": "The problem of faithfulness of the (reduced) Burau representation for $n =4$ is known to be equivalent to the problem of whether certain two matrices A and B generate a free group of rank two. In [Ber-Tra] we gave a simple proof that $(A^3, B^3)$ is a free group of rank two, the result known earlier from [Wil-Zar]. In this paper we use a combination of methods of linear algebra and homology theory (the forks and noodles approach) to give another proof that $(A^3, B^3)$ is a free group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-26T09:17:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F29",
      "20F36"
    ],
    "keywords": [
      "burau representation",
      "free group",
      "linear algebra",
      "noodles approach",
      "homology theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}