{
  "annotation_id": "061e9cc7-b6cb-4e06-a932-3040bf8077f4",
  "date_created": "2026-02-17T05:53:08.871000Z",
  "date_modified": "2026-02-17T05:53:08.871000Z",
  "file_hash": "872a55c24c0961988bf4e6a19216cc448c2a84fe24201e8ca2834108227946cc",
  "private": false,
  "record": {
    "abstract": "For $\\pi$ a finitely presented group, Hausmann and Weinberger defined $q(\\pi) \\in \\mathbb Z$ to be the minimum Euler characteristic over all closed, oriented $4$-manifolds with fundamental group $\\pi$. This short note establishes that this minimum value in general differs depending on whether one minimizes over topological manifolds or only those admitting a smooth structure.",
    "arxiv_id": "2601.07040",
    "authors": [
      "Mike Miller Eismeier"
    ],
    "categories": [
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "title": "The topological and smooth Hausmann-Weinberger invariants disagree",
    "url": "https://arxiv.org/abs/2601.07040",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cf99dc5f-db15-477d-812e-d6a2930918e3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}