{
  "id": "2006.01810",
  "version": "v1",
  "published": "2020-06-02T17:46:00.000Z",
  "updated": "2020-06-02T17:46:00.000Z",
  "title": "Motive of the $SL_4$-character variety of torus knots",
  "authors": [
    "Angel González-Prieto",
    "Vicente Muñoz"
  ],
  "comment": "35 pages. Note: download source for the output of all the strata as separate file",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "In this paper, we compute the motive of the character variety of representations of the fundamental group of the complement of an arbitrary torus knot into $SL_4(k)$, for any algebraically closed field $k$. For that purpose, we introduce a stratification of the variety in terms of the type of a canonical filtration attached to any representation. This allows us to reduce the computation of the motive to a combinatorial problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-02T17:46:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "57M25",
      "57M27"
    ],
    "keywords": [
      "character variety",
      "arbitrary torus knot",
      "fundamental group",
      "representation",
      "combinatorial problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}