{
  "abstract": "Let $X$ be an oriented topological $4$-manifold with boundary. We establish a Dax isomorphism for the fundamental group of the space of embedded arcs in $X$. Here, the embedding space can be either the simplicial set of locally flat embeddings or the space of topological embeddings endowed with the compact-open topology. When $X$ is smooth, we show that the space of smooth arcs and topological arcs have canonically isomorphic fundamental groups, and the topological Dax isomorphism agrees with the smooth Dax isomorphism. As a consequence, the homomorphisms that arise in the smooth Dax isomorphism do not depend on the smooth structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15792",
  "author_total": 3,
  "authors": [
    {
      "name": "Jianfeng Lin"
    },
    {
      "name": "Yi Xie"
    },
    {
      "name": "Boyu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wn2k0nnymvz7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15792",
  "fulltext_url": null,
  "id": "4wn2k0nnymvz7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15792",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213337679",
  "pdf_url": "https://arxiv.org/pdf/2609.15792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wn2k0nnymvz7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Dax isomorphism for topological $4$-manifolds",
  "title_text": "The Dax isomorphism for topological $4$-manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4wn2k0nnymvz7",
  "venue": "arXiv",
  "versions": []
}