A skein approach to Bennequin type inequalities
Lenhard Ng
TL;DR
This paper presents a unified proof technique for various bounds on Thurston-Bennequin and self-linking numbers of Legendrian and transverse knots, offering a template for future bounds and conditions for sharpness.
Contribution
It introduces a skein-based approach that unifies multiple bounds and provides a framework for deriving new inequalities in knot theory.
Findings
Unified proof for several bounds on Thurston-Bennequin and self-linking numbers
Template for future bounds on Legendrian and transverse knots
Conditions identified for bounds to be sharp
Abstract
We give a simple unified proof for several disparate bounds on Thurston-Bennequin number for Legendrian knots and self-linking number for transverse knots in R^3, and provide a template for possible future bounds. As an application, we give sufficient conditions for some of these bounds to be sharp.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Supramolecular Self-Assembly in Materials