Work

Non‐isotopic splitting spheres for a split link in S4$S^4$

Year: 2025

Type: article

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 .

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70038

Authors: Mark Hughes, Seungwon Kim, Maggie Miller

Institutions: Brigham Young University, Sungkyunkwan University, The University of Texas at Austin

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,700

Funders: National Science Foundation, Simons Foundation, National Research Foundation of Korea