Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Relative Khovanov–Jacobsson classes

Isaac Sundberg and Jonah Swann

Algebraic & Geometric Topology 22 (2022) 3983–4008
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 946, and is not hindered by detecting connected sums with knotted 2–spheres.

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