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
Knotted handlebodies in the 4-sphere and 5-ball cover

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Abstract

For every integer we construct 3-dimensional genus- 1-handlebodies smoothly embedded in 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 . 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