Non‐isotopic splitting spheres for a split link in S4$S^4$
Abstract We show that there exist split, orientable, 2‐component surface‐links in with non‐isotopic splitting spheres in their complements. In particular, for non‐negative integers with , the unlink consisting of one component of genus and one component of genus contains in its complement two smooth splitting spheres that are not topologically isotopic in . This contrasts with link theory in the classical dimension, as any two splitting spheres in the complement of a 2‐component split link are isotopic in .
Authors
- Seungwon Kim (ORCID: https://orcid.org/0000-0001-8948-6622)
- Mark Hughes (ORCID: https://orcid.org/0000-0003-3278-130X)
- Maggie Miller (ORCID: https://orcid.org/0000-0002-1669-1956)
Institutions
- Brigham Young University (US)
- Sungkyunkwan University (KR)
- The University of Texas at Austin (US)
Publication Details
- Journal
- Proceedings of the London Mathematical Society
- Published
- 2025-04-01
- DOI
- https://doi.org/10.1112/plms.70038
- Citations
- 1
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- National Science Foundation
- Simons Foundation
- National Research Foundation of Korea