{
  "abstract": "Let $M$ be a closed, smooth or topological $n$-manifold, with $n \\geq 4$. We construct a homotopy highly cartesian square relating the space ${\\mathcal E}(M (\\ell))$ of homotopy self-equivalences of $M$ (in a suitable range) over the Postnikov $\\ell$-sections of its stable normal microbundle, and an $(\\infty + n)$-fold loop space representing an associated (normal) bordism theory. This implies the existence of braids of interlocking exact sequences involving the homotopy groups of ${\\mathcal E}(M(\\ell))$ and certain Lashof bordism groups, leading to a conceptual explanation and broad generalization of earlier work of Hambleton--Kreck for closed, oriented $4$-manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11110",
  "author_total": 2,
  "authors": [
    {
      "name": "Ian Hambleton"
    },
    {
      "name": "Kursat Sozer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a24txyv88wtxp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11110",
  "fulltext_url": null,
  "id": "a24txyv88wtxp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11110",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7221158147",
  "pdf_url": "https://arxiv.org/pdf/2610.11110",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a24txyv88wtxp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11110",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11110"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Braidings of Self-Equivalences and Bordism",
  "title_text": "Braidings of Self-Equivalences and Bordism",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/a24txyv88wtxp",
  "venue": "arXiv",
  "versions": []
}