{
  "id": "1405.0816",
  "version": "v2",
  "published": "2014-05-05T08:07:14.000Z",
  "updated": "2015-09-12T21:15:12.000Z",
  "title": "E-polynomial of the SL(3,C)-character variety of free groups",
  "authors": [
    "Sean Lawton",
    "Vicente Muñoz"
  ],
  "comment": "21 pages; accepted for publication at the Pacific Journal of Mathematics",
  "categories": [
    "math.AG"
  ],
  "abstract": "We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3, C). Expanding upon existing techniques, we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give new proofs of the SL(2,C), PGL(2,C), and PGL(3,C) cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-05T08:07:14.000Z",
      "abstract": "We compute the E-polynomial of the character variety of representations of the free group F in the group SL(3,C) by stratifying the space of representations and computing the E-polynomial of each geometrically described stratum using fibrations. Along the way, we give new proofs of the SL(2,C), PGL(2,C), and PGL(3,C) cases.",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-12T21:15:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "20C15",
      "14L30",
      "20E05"
    ],
    "keywords": [
      "free group",
      "e-polynomial",
      "representations",
      "group sl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0816L"
    }
  }
}