{
  "annotation_id": "825f5327-7cc3-49a5-b079-6f9e971b9884",
  "date_created": "2026-03-02T18:01:28.716000Z",
  "date_modified": "2026-03-02T18:01:28.716000Z",
  "file_hash": "11d5eac2d8bc8498bad476bc0ccaf71ceb76ca2da0f131d4f0afeb38cb9c7526",
  "private": false,
  "record": {
    "abstract": "Given an oriented knot K in S^3 and a TQFT, Turaev and Viro defined modules\nsomewhat analogous to the Alexander module. We work with the (V_p,Z_p) theories\nof Blanchet, Habegger, Masbaum and Vogel {BHMV} for p \\ge 3, and consider the\nassociated modules. In {G}, we defined modules which also depend on the extra\ndata of a color c which is assigned to a meridian of the knot in the\nconstruction of the module. These modules can be used to calculate the quantum\ninvariants of cyclic branched covers of knots and have other uses. Suppose now\nthat S is a satellite knot with companion C, and pattern P. We give formulas\nfor the Turaev-Viro modules for S in terms of the Turaev-Viro modules of C and\nsimilar data coming from the pattern P. We compute these invariants explicitly\nin several examples.",
    "arxiv_id": "q-alg/9610015",
    "authors": [
      "Patrick M. Gilmer"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "journal_ref": "Knots 96, ed S. Suzuki, World Scientific 1997, 337-363",
    "title": "Turaev-Viro Modules of Satellite knots",
    "url": "https://arxiv.org/abs/q-alg/9610015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f77d67fc-250f-48ff-a8c4-270365aee04a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}