{
  "abstract": "Farrell and Jones showed that negatively curved manifolds in dimension $\\geq 5$ are topologically rigid in the sense that homotopy equivalence implies homeomorphism. In the smooth category, the result does not hold even for hyperbolic manifolds, and there are negatively curved manifolds $N$ homotopy equivalent to a given hyperbolic manifold $M$ but not diffeomorphic. For complex hyperbolic manifolds, the analogous construction is demonstrated only in dimensions of the form $8n+2$. In this paper, we prove this result in many other dimensions. The main approach involves the use of $EO$-theory of complex projective spaces to construct suitable examples of exotic spheres. These theories may be viewed as a version of real $K$-theory, and are defined at each prime $p$. The computation also yields positive results about the existence of free smooth $S^1$ and $S^3$ actions on exotic spheres which do not bound parallelizable manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10070",
  "author_total": 2,
  "authors": [
    {
      "name": "Samik Basu"
    },
    {
      "name": "Akashdwip Biswas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3xhnpatxa4c3b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10070",
  "fulltext_url": null,
  "id": "3xhnpatxa4c3b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10070",
  "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",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221043792",
  "pdf_url": "https://arxiv.org/pdf/2610.10070",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3xhnpatxa4c3b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10070",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10070"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Exotic structures on hyperbolic manifolds via the EO-theory of Projective Spaces",
  "title_text": "Exotic structures on hyperbolic manifolds via the EO-theory of Projective Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/3xhnpatxa4c3b",
  "venue": "arXiv",
  "versions": []
}