{
  "annotation_id": "cf655ea2-89b5-4d50-b49e-0e82788abfc8",
  "date_created": "2026-02-17T05:53:20.293000Z",
  "date_modified": "2026-02-17T05:53:20.293000Z",
  "file_hash": "b82ba1950de20223647437d2113b81832f64e6fcd1269abac80389a16be11b15",
  "private": false,
  "record": {
    "abstract": "We consider the realisation problem for normal 1-types of 4-manifolds with a given boundary. More precisely, given a normal 1-type $\\xi$ and closed 3-dimensional $\\xi$-manifold $Y$, does there exist a compact 4-dimensional $\\xi$-manifold with boundary $Y$? We describe a three stage obstruction theory for the existence of such a 4-manifold, with our main contribution being a `tertiary\u0027 obstruction that we describe geometrically via Wall\u0027s quadratic self-intersection form.",
    "arxiv_id": "2601.09650",
    "authors": [
      "Daniel Galvin",
      "Peter Teichner",
      "Simona Vesel\u00e1"
    ],
    "categories": [
      "math.GT",
      "math.AT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Geometric obstructions for $\\xi$-fillings of 3-manifolds",
    "url": "https://arxiv.org/abs/2601.09650",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ad803917-fa82-472f-a9b4-c6ceb4d452b6",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}