Khovanov homology and refined bounds for Gordian distances
Lukas Lewark, Laura Marino, Claudius Zibrowius
TL;DR
This paper introduces a new lower bound for the Gordian distance of knots derived from Khovanov homology, enhancing existing bounds from Rasmussen invariants and torsion invariants, and also improves bounds for rational Gordian distance.
Contribution
The authors develop a refined lower bound for Gordian distances using Khovanov homology, unifying and strengthening previous invariants and extending to rational Gordian distances.
Findings
New lower bound for knot Gordian distance from Khovanov homology
Strengthened bounds combining Rasmussen and torsion invariants
Improved bounds for rational Gordian distance
Abstract
From Khovanov homology, we extract a new lower bound for the Gordian distance of knots, which combines and strengthens the previously existing bounds coming from Rasmussen invariants and from torsion invariants. We also improve the bounds for the proper rational Gordian distance.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis