Distinguishing slice disks using knot Floer homology

Author: 

Juhasz, A
Zemke, I

Publication Date: 

21 December 2019

Journal: 

Selecta Mathematica

Last Updated: 

2020-10-04T15:46:48.49+01:00

Issue: 

1

Volume: 

26

DOI: 

10.1007/s00029-019-0531-6

abstract: 

We study the classification of slice disks of knots up to isotopy and diffeomorphism using an invariant in knot Floer homology. We compute the invariant of a slice disk obtained by deform-spinning, and show that it can be effectively used to distinguish non-isotopic slice disks with diffeomorphic complements. Given a slice disk of a composite knot, we define a numerical stable diffeomorphism invariant called the rank. This can be used to show that a slice disk is not a boundary connected sum, and to give lower bounds on the complexity of certain hyperplane sections of the slice disk.

Symplectic id: 

1077242

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article