Knotted handlebodies in the 4-sphere and 5-ball

Mark Hughes; Seungwon Kim; Maggie Miller

doi:10.4171/jems/1534

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Knotted handlebodies in the 4-sphere and 5-ball

Mark Hughes
Brigham Young University, Provo, USA
Seungwon Kim
Sungkyunkwan University, Seoul, South Korea
Maggie Miller
The University of Texas at Austin, Austin, USA

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Abstract

For every integer $g \geq 2$ we construct 3-dimensional genus- $g$ 1-handlebodies smoothly embedded in $S^{4}$ 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 $B^{5}$ . This proves a conjecture of Budney–Gabai for genus at least 2.

Cite this article

Mark Hughes, Seungwon Kim, Maggie Miller, Knotted handlebodies in the 4-sphere and 5-ball. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1534