{
  "id": "1302.1632",
  "version": "v2",
  "published": "2013-02-07T02:50:28.000Z",
  "updated": "2014-09-25T01:39:10.000Z",
  "title": "Twisted Alexander polynomials with the adjoint action for some classes of knots",
  "authors": [
    "Anh T. Tran"
  ],
  "comment": "9 pages, 1 figure. To appear in Journal of Knot Theory and Its Ramifications",
  "categories": [
    "math.GT"
  ],
  "abstract": "We calculate the twisted Alexander polynomial with the adjoint action for torus knots and twist knots. As consequences of these calculations, we obtain the formula for the nonabelian Reidemeister torsion of torus knots in \\cite{Du} and a formula for the nonabelian Reidemeister torsion of twist knots that is better than the one in \\cite{DHY}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-07T02:50:28.000Z",
      "abstract": "This paper studies the twisted Alexander polynomial with the adjoint action associated to SL_2(C)-representations of a knot group for some classes of knots. We explicitly calculate the twisted Alexander polynomial with the adjoint action for torus knots and twist knots. As consequences of these calculations, we obtain the formula of the non-abelian Reidemeister torsion for torus knots in [Du] and a nicer formula of the non-abelian Reidemeister torsion for twist knots than the one in [DHY].",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-25T01:39:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "twisted alexander polynomial",
      "adjoint action",
      "non-abelian reidemeister torsion",
      "twist knots",
      "torus knots"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1632T"
    }
  }
}