{
  "id": "2405.18557",
  "version": "v1",
  "published": "2024-05-28T20:04:28.000Z",
  "updated": "2024-05-28T20:04:28.000Z",
  "title": "Skein modules and character varieties of Seifert manifolds",
  "authors": [
    "Renaud Detcherry",
    "Efstratia Kalfagianni",
    "Adam S. Sikora"
  ],
  "comment": "28 pages",
  "categories": [
    "math.GT",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold $M$ is finitely generated over $\\mathbb Z[A^{\\pm 1}]$ if and only if $M$ is irreducible and non-Haken. We analyze in detail the character varieties $X(M)$ of such manifolds and show that under mild conditions they are reduced. We compute the Kauffman bracket skein modules for these $3$-manifolds (over $\\mathbb Q(A)$) and show that their dimensions coincide with $|X(M)|.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-28T20:04:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K31",
      "57K16"
    ],
    "keywords": [
      "character varieties",
      "kauffman bracket skein module",
      "seifert manifolds",
      "mild conditions",
      "dimensions coincide"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}