Non-loose Legendrian Hopf links in lens spaces

TL;DR

This paper classifies non-loose Legendrian Hopf links in lens spaces, providing a comprehensive understanding of their structure and an explicit algorithm for contact surgery diagrams, extending previous work to include cases with and without Giroux torsion.

Contribution

It offers a complete classification of non-loose Legendrian Hopf links in lens spaces, including cases with Giroux torsion, and presents an explicit algorithm for contact surgery diagrams.

Findings

Classification of non-loose Legendrian Hopf links in lens spaces.

Explicit contact surgery diagram algorithm for these links.

Extension of previous results to include Giroux torsion cases.

Abstract

We give a complete classification of non-loose Legendrian Hopf links in $L(p,q)$ generalizing a result of the author with Geiges and Onaran. The classification is for non-loose Hopf links for both zero and non-zero Giroux torsion in their complement. We also give an explicit algorithm for the contact surgery diagrams for all these Legendrian representatives with no Giroux torsion in their complement.