{
  "annotation_id": "1321a0ca-18a0-40c1-b66b-53286ef5c89f",
  "date_created": "2026-03-02T18:01:28.472000Z",
  "date_modified": "2026-03-02T18:01:28.472000Z",
  "file_hash": "049c8b5f3e286e8fb6cd7d216404674945aeddad201f4c8355010cf1646c787e",
  "private": false,
  "record": {
    "abstract": "Using the recently developed theory of finite type invariants of integral\nhomology 3-spheres we study the structure of the Torelli group of a closed\nsurface. Explicitly, we construct (a) natural cocycles of the Torelli group\n(with coefficients in a space of trivalent graphs) and cohomology classes of\nthe abelianized Torelli group; (b) group homomorphisms that detect (rationally)\nthe nontriviality of the lower central series of the Torelli group. Our results\nare motivated by the appearance of trivalent graphs in topology and in\nrepresentation theory and the dual role played by the Casson invariant in the\ntheory of finite type invariants of integral homology 3-spheres and in Morita\u0027s\nstudy of the structure of the Torelli group Our results generalize those of S.\nMorita {Mo1,Mo2} and complement the recent calculation, due to R. Hain, of the\nI-adic completion of the rational group ring of the Torelli group. We also give\nanalogous results for two other subgroups of the mapping class group.",
    "arxiv_id": "q-alg/9603013",
    "authors": [
      "Stavros Garoufalidis",
      "Jerome Levine"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Finite type 3-manifold invariants and the structure of the Torelli group   I",
    "url": "https://arxiv.org/abs/q-alg/9603013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "26c20186-41d1-47b4-b95e-ec4f87cce2f4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}