{
  "abstract": "Given a smooth manifold, a tangential $O\\langle n \\rangle$-structure is a lift of the classifying map of its tangent bundle to $BO\\langle n \\rangle$. An $O\\langle n \\rangle$-manifold is a manifold equipped with an equivalence class of tangential $O\\langle n \\rangle$-structures. The cases $n=2$ and $n=4$ recover the familiar notions of oriented and spin manifolds. Larger values of $n$ furnish higher analogs of these with additional geometric properties. In this thesis, we calculate the 2-primary component of the cobordism groups of compact $O\\langle n\\rangle $-manifolds in a range of degrees, for $n$ between 9 and 17. We derive various consequences for the boundaries of almost-closed manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28804",
  "author_total": 1,
  "authors": [
    {
      "name": "Hassan H. Abdallah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/asaesvdnbkv11.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28804",
  "fulltext_url": null,
  "id": "asaesvdnbkv11",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28804",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214282406",
  "pdf_url": "https://arxiv.org/pdf/2609.28804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/asaesvdnbkv11.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28804"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the cobordism groups of $O\\langle n\\rangle$-manifolds",
  "title_text": "On the cobordism groups of O⟨ n⟩-manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/asaesvdnbkv11",
  "venue": "arXiv",
  "versions": []
}