{
  "id": "1509.03277",
  "version": "v1",
  "published": "2015-09-10T19:00:54.000Z",
  "updated": "2015-09-10T19:00:54.000Z",
  "title": "Character varieties, A-polynomials, and the AJ Conjecture",
  "authors": [
    "Thang T. Q. Le",
    "Xingru Zhang"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We establish some facts about the behavior of the rational-geometric subvariety of the $SL_2(\\c)$ or $PSL_2(\\c)$ character variety of a hyperbolic knot manifold under the restriction map to the $SL_2(\\c)$ or $PSL_2(\\c)$ character variety of the boundary torus, and use the results to get some properties about the A-polynomials and to prove the AJ conjecture for certain class of knots in $S^3$ including in particular any $2$-bridge knot over which the double branched cover of $S^3$ is a lens space of prime order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-10T19:00:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "character variety",
      "aj conjecture",
      "a-polynomials",
      "hyperbolic knot manifold",
      "boundary torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150903277L"
    }
  }
}