{
  "annotation_id": "962b6349-cdca-4bb6-a2eb-f3f5fa23e4d7",
  "date_created": "2026-02-17T05:53:05.005000Z",
  "date_modified": "2026-02-17T05:53:05.005000Z",
  "file_hash": "352e1ff91dba9e37da83fcb49569e0ad40e4025fd9f51e670ee0b633e6c9d373",
  "private": false,
  "record": {
    "abstract": "Let $M$ and $N$ be smooth closed connected aspherical manifolds with good (in the sense of Serre) fundamental groups $G$ and $H$. We show that if $\\widehat G\\cong \\widehat H$, then $M$ and $N$ are cobordant and the signatures of $M$ and $N$ agree modulo $8$. Moreover, $M$ is spin (resp.spin$^\\CC$) if and only if $N$ is spin (resp.spin$^\\CC$). We consider some analogous results for compact connected aspherical manifolds.",
    "arxiv_id": "2601.05706",
    "authors": [
      "Sam Hughes",
      "Andrew Ng"
    ],
    "categories": [
      "math.GR",
      "math.AT",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Cobordism, spin structures, and profinite completions",
    "url": "https://arxiv.org/abs/2601.05706",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3a662623-d8ff-4b0b-907d-7803d3a6c201",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}