Legendrian Negative Torus Knots in Universally Tight Lens Spaces

TL;DR

This paper classifies all Legendrian negative torus knots in universally tight lens spaces using convex Heegaard decompositions, completing the classification of Legendrian torus knots in such spaces.

Contribution

It provides a complete classification of Legendrian negative torus knots in universally tight lens spaces, extending previous results to include all Legendrian torus knots.

Findings

Characterization of Legendrian negative torus knots in lens spaces

Complete classification of Legendrian torus knots in universally tight lens spaces

Use of convex Heegaard decomposition as the main method

Abstract

The main theorem characterizes all Legendrian negative torus knots in universally tight lens space in the sense of coarse equivalence. Together with Onaran's results on Legendrian positive torus knots, all Legendrian torus knots in universally tight lens space is classified. The main method is splitting L(p, q) by convex Heegaard decomposition.