Relative Knot Invariants: Properties and Applications

TL;DR

This paper explores relative knot invariants, establishing inequalities, their additive properties, limitations, and classification results for relatively Legendrian simple knots.

Contribution

It extends classical knot invariants to the relative case, providing new inequalities, additive properties, and classification insights.

Findings

Relative invariants satisfy Bennequin inequalities.

They are additive under relative connected sums.

Limitations similar to classical invariants are observed.

Abstract

We state Bennequin inequalities in the relative case, and show that the relative invariants are additive under relative connected sums. We show they exhibit similar limitations as their classical analogues. We study relatively Legendrian simple knots and give some classification results.