{
  "abstract": "We investigate the realisability of the Casson–Sullivan invariant for homeomorphisms of smooth 4-manifolds, which is the obstruction to a homeomorphism being stably pseudo-isotopic to a diffeomorphism, valued in the third cohomology of the source manifold with double struck upper Z divided by 2 Z / 2 $\\mathbb{Z}/2$ -coefficients. We prove that for all pairs of orientable, homeomorphic, smooth 4-manifolds this invariant can be realised fully after stabilising with a single upper S squared times upper S squared S 2 × S 2 $S^2\\times S^2$ . As an application, we obtain that topologically isotopic surfaces in a smooth, simply-connected 4-manifold become smoothly isotopic after sufficient external stabilisations. We further demonstrate cases where this invariant can be realised fully without stabilisation for self-homeomorphisms, which includes for manifolds with finite cyclic fundamental group. This method allows us to produce many examples of homeomorphisms which are not stably pseudo-isotopic to any diffeomorphism but are homotopic to the identity. Finally, we reinterpret these results in terms of finding examples of smooth structures on 4-manifolds which are diffeomorphic but not stably pseudo-isotopic.",
  "abstract_shown": true,
  "affiliations": [
    "University of Texas at Austin"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Daniel Galvin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cftrnsxs72dag.bib",
  "cited_by": 13,
  "doi": "10.1017/s0010437x26103510",
  "fulltext_url": null,
  "id": "cftrnsxs72dag",
  "issns": [
    "0010-437X",
    "1570-5846"
  ],
  "landing_url": "https://doi.org/10.1017/s0010437x26103510",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
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  "openalex": "W4396914128",
  "pdf_url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8376A5449442D18DD6C9E39C587849CA/S0010437X26103510a.pdf/div-class-title-the-casson-sullivan-invariant-for-homeomorphisms-of-4-manifolds-div.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": "Cambridge University Press",
  "ris": "https://research.draconitic.com/paper/cftrnsxs72dag.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T13:20:36Z",
      "native_id": "W4396914128",
      "source": "openalex",
      "url": "https://doi.org/10.1017/s0010437x26103510"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Geometric and Algebraic Topology",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Casson–Sullivan invariant for homeomorphisms of 4-manifolds",
  "title_text": "The Casson–Sullivan invariant for homeomorphisms of 4-manifolds",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/cftrnsxs72dag",
  "venue": "Compositio Mathematica",
  "versions": []
}