{
  "abstract": "We give an infinite family of non-diffeomorphic exotic $\\mathbb{R}^4$'s, each of which is the union of two copies of a standard open tubular neighborhood of the circle, which intersect in a standard open tubular neighborhood of the wedge of two circles. This gives the simplest known decomposition of an exotic $\\mathbb{R}^4$ into two open sets, making progress on Question 4.43 (A) of Kirby's 1995 problem list. The decompositions are obtained by studying fibered slice disk complements in certain Casson-Gordon homotopy 4-balls, for which we provide similar decompositions. We distinguish the $\\mathbb{R}^4$'s using end Floer homology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19263",
  "author_total": 1,
  "authors": [
    {
      "name": "Sean Eli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53cc6rqx23hfn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19263",
  "fulltext_url": null,
  "id": "53cc6rqx23hfn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19263",
  "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": "W7222136387",
  "pdf_url": "https://arxiv.org/pdf/2610.19263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53cc6rqx23hfn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19263"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Exotic $\\mathbb{R}^4$'s as unions of two thickened circles",
  "title_text": "Exotic ℝ^4's as unions of two thickened circles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/53cc6rqx23hfn",
  "venue": "arXiv",
  "versions": []
}