Unknotting 3-balls in the 5-ball

Daniel Hartman

Published 2022-06-22Version 1

The purpose of this note is to answer affirmatively a question posed by both Gay, and Hughes, Kim and Miller as to whether every $3$--ball smoothly embedded in the $4$--sphere becomes isotopic relative to the bounding 2-sphere when pushed into the 5-ball. In fact, we show that any two collections of disjointly embedded smooth $3$--balls bounding an unlink of 2--spheres in $S^4$ are isotopic relative to the unlink when pushed into the $5$--ball.