Knotted handlebodies in the 4-sphere and 5-ball

Mark Hughes; Seungwon Kim; Maggie Miller

Knotted handlebodies in the 4-sphere and 5-ball

Geometric Topology 2023-07-04 v4

Authors: Mark Hughes , Seungwon Kim , Maggie Miller

Abstract

For every integer $g\ge 2$ 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.

Keywords

knotted handlebodies 4-sphere 5-ball locally flat isotopy cut systems genus-g 1-handlebodies Budney-Gabai conjecture

Cite

@article{arxiv.2111.13255,
  title  = {Knotted handlebodies in the 4-sphere and 5-ball},
  author = {Mark Hughes and Seungwon Kim and Maggie Miller},
  journal= {arXiv preprint arXiv:2111.13255},
  year   = {2023}
}

Comments

11 pages, 3 figures. Various minor changes were made in this version to address referee comments. This version has been accepted for publication in the Journal of the European Mathematical Society

Knotted handlebodies in the 4-sphere and 5-ball

Abstract

Keywords

Cite

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