{
  "abstract": "We show that the Torelli group of a simply connected closed 5-manifold $M$, which is spin and has no 2-torsion elements in homology, is isomorphic to the bordism group $Ω^{\\mathrm{Spin}}_6(K(H_2(M), 2))$. For $H_2(M)$ with no 2- and 3-torsion we determine this bordism group, and give explicit constructions for the generators of the Torelli group. Furthermore, for the $g$-fold connected sum ${\\#}^g(S^2 \\times S^3)$ we completely determine its mapping class group. We apply our results to compute the stabilization and abelianization of the mapping class group of ${\\#}^g(S^2 \\times S^3)$, determine the group of isotopy classes of diffeomorphisms of $M$ that are homotopic to the identity, and study the embeddings of $S^3$ in $S^2 \\times S^3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26698",
  "author_total": 1,
  "authors": [
    {
      "name": "Huize Jin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rffgqdfqtmft.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26698",
  "fulltext_url": null,
  "id": "1rffgqdfqtmft",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26698",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204532155",
  "pdf_url": "https://arxiv.org/pdf/2608.26698",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rffgqdfqtmft.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2608.26698",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26698"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology",
  "title_text": "Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1rffgqdfqtmft",
  "venue": "arXiv",
  "versions": []
}