{
  "annotation_id": "f983486f-c7e4-46a0-91e1-d7c124ec3546",
  "date_created": "2026-03-02T18:01:24.713000Z",
  "date_modified": "2026-03-02T18:01:24.713000Z",
  "file_hash": "52ce970891b7824079785997a03e0ca8bcc7c03451becca8a7755e26f9a625d3",
  "private": false,
  "record": {
    "abstract": "Given a positive integer $n$, we say that two knots are $V_n$-equivalent if\nthey have the same Vassiliev invariants of order $\\le n$. We showed that the\n$V_n$-equivalence classes of ribbon knots form a group, the operation being\ninduced by the connected sums of knots. The group is free abelian and its rank\nis equal to the dimension of the space of primitive Vassiliev invariants of\norder $\\le n$. The $n$-equivalence classes (following Gusarov\u0027s notion) of\nribbon knots also constitute a group. As a corollary, any non-ribbon knot whose\nArf invariant istrivial cannot be distinguished from ribbon knots by finitely\nmany Vassiliev invariants. Furthermore, all additive knot cobordism invariants\nare not of finite type. As a bi-product, we prove that the number of\nindependent Vassiliev invariants of order $n$ is bounded above by $(n-2)!/2$\nfor $n\u003e5$.",
    "arxiv_id": "q-alg/9502017",
    "authors": [
      "Ka Yi Ng"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Groups of ribbon knots",
    "url": "https://arxiv.org/abs/q-alg/9502017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f4f5ca7f-62f3-4265-9bc1-2a4ef92837af",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}