{
  "annotation_id": "766fad6c-caca-471b-afad-84408a20a65c",
  "date_created": "2026-02-17T05:53:15.943000Z",
  "date_modified": "2026-02-17T05:53:15.943000Z",
  "file_hash": "4e9bde6b9f3b072d757ff4d8986c38bca57ebe058bd66d22275a79a4e2457f41",
  "private": false,
  "record": {
    "abstract": "We construct a natural chain map from the Kontsevich graph complex to the rational singular chain complex of $B\\mathrm{Diff}_\\partial(D^{2k})$ when the dimension $2k$ is sufficiently large, generalizing Goussarov and Habiro\u0027s theories of surgery on 3-valent graphs in 3-manifolds. Our construction can be considered as a topological realization of the Kontsevich graph complex. We also give new constructions of elements in the rational homotopy groups of $B\\mathrm{Diff}_\\partial(D^{2k})$ which are determined by well-known cycles in the graph complex.",
    "arxiv_id": "2601.08200",
    "authors": [
      "Boris Botvinnik",
      "Tadayuki Watanabe"
    ],
    "categories": [
      "math.GT",
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Brunnian links and Kontsevich graph complex I",
    "url": "https://arxiv.org/abs/2601.08200",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "025f2806-ffcc-4558-a8a3-1845d7730bec",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}