Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 8 min ago
PreprintCC BY-NC-SA 4.0arXiv

The Dax isomorphism for topological $4$-manifolds

  • Jianfeng Lin
  • Yi Xie
  • Boyu Zhang
Open at sourcePDFDOICite

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.

Related

  1. A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds
    Maria Morariu
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. Topological isomorphism of procountable groups is universal analytic
    Xinan Dai, Wenhao Deng, Yingdong Shi +2
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Smoothing topological isotopy of surfaces in 4-manifolds with a boundary geometric dual
    Jae Choon Cha, Byeorhi Kim
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. Topological and spectral rigidity of hypersurface Zoll manifolds
    Gustavo Martins
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. A non-perturbative topological persistence theorem for normally hyperbolic invariant manifolds
    Wojciech Spólnik, Maciej J. Capiński
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{lin2026isomorphism,
  title = {{The Dax isomorphism for topological $4$-manifolds}},
  author = {Jianfeng Lin and Yi Xie and Boyu Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15792},
  eprint = {2609.15792},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15792},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - The Dax isomorphism for topological $4$-manifolds
AU  - Jianfeng Lin
AU  - Yi Xie
AU  - Boyu Zhang
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15792
UR  - https://arxiv.org/abs/2609.15792
AB  - 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.
ER  -