Positivities of knots and links and the defect of Bennequin inequality
Jesse Hamer, Tetsuya Ito, and Keiko Kawamuro
TL;DR
This paper explores the relationships among different positivity properties of knots and links, provides evidence for conjectures related to the Bennequin inequality defect, and classifies positivity types for knots up to 12 crossings.
Contribution
It offers new insights into the connections between various positivity notions and the Bennequin inequality, and provides classifications for knots up to 12 crossings.
Findings
Supported conjectures on positivity and Bennequin inequality defect
Classified strong quasipositivity and quasipositivity for knots up to 12 crossings
Identified exceptions in quasipositivity classification
Abstract
We discuss relations among various positivities of knots and links, such as strong quasipositivity and quasipositivity. We give several pieces of supporting evidence for conjectural statements concerning these positivities and the defect of Bennequin inequality. Finally, we determine strong quasipositivity and quasipositivity for knots up to 12 crossings (with two exceptions for quasipositivity).
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