Knotted handlebodies in the 4-sphere and 5-ball

2021/11/25 by Mark Hughes, Hughes, Mark, Seungwon Kim +3 · 1 citation
Computer Science · Mathematics · #57K45 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2111.13255

openalex publication_date 2021/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every integer g≥ 2 we construct 3-dimensional genus-g 1-handlebodies smoothly embedded in S⁴ with the same boundary, and which are defined by the same cut systems of their boundary, yet which are not isotopic rel. boundary via any locally flat isotopy even when their interiors are pushed into B⁵. This proves a conjecture of Budney-Gabai for genus at least 2.

Cited by

• Spanning 3-discs in the 4-sphere pushed into the 5-disc

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