Unknotting number and cabling
Abstract
abstract: The unknotting number of knots is a difficult quantity to compute, and even its behavior under basic satelliting operations is not understood. We establish a lower bound on the unknotting number of cable knots and iterated cable knots purely in terms of the winding number of the pattern. The proof uses Alishahi--Eftekhary's bounds on unknotting number from knot Floer homology together with Hanselman--Watson's computation of the knot Floer homology of cables in terms of immersed curves in the punctured torus.
Fields of Study & Subjects
Geometric and Algebraic Topology
Publication details
- Journal / source
- American Journal of Mathematics
- Volume
- 148
- Issue
- 4
- Pages
- 961–984
- Publication date
- 1 August 2026
- Language
- EN