Relative Khovanov–Jacobsson classes

Sundberg, Isaac; Swann, Jonah

doi:10.2140/agt.2022.22.3983

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Relative Khovanov–Jacobsson classes

Isaac Sundberg and Jonah Swann

Algebraic & Geometric Topology 22 (2022) 3983–4008

DOI: 10.2140/agt.2022.22.3983

Abstract

Given a smooth, compact, oriented, properly embedded surface in the $4$ –ball, we define an invariant of its boundary-preserving isotopy class from the Khovanov homology of its boundary link. Previous work showed that when the boundary link is empty, this invariant is determined by the genus of the surface. We show that this relative invariant can obstruct sliceness of knots, detects a pair of slices for $9_{46}$ , and is not hindered by detecting connected sums with knotted $2$ –spheres.

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Keywords

slice disks, smooth isotopy, relative Khovanov-Jacobsson classes, Khovanov homology

Mathematical Subject Classification

Primary: 57K18, 57R52, 57K16, 57R40

References

Publication

Received: 3 March 2021

Revised: 24 June 2021

Accepted: 2 September 2021

Published: 14 March 2023

Authors

Isaac Sundberg
Bryn Mawr College Bryn Mawr, PA United States
https://imsundberg.github.io/
Jonah Swann
Arden, NC United States

Volume 22, issue 8 (2022)