arXiv Analytics

Sign in

arXiv:2206.11243 [math.GT]AbstractReferencesReviewsResources

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.

Comments: 6 pages, 3 figures
Categories: math.GT
Subjects: 57R52, 57K45
Related articles:
arXiv:2205.03474 [math.GT] (Published 2022-05-06)
The Jones polynomial of collections of open curves in 3-space
arXiv:math/0612796 [math.GT] (Published 2006-12-27)
Dissecting the 2-sphere by immersions
arXiv:1901.04734 [math.GT] (Published 2019-01-15)
Torsions and intersection forms of 4-manifolds from trisection diagrams