Legendrian rational unknots in lens spaces

TL;DR

This paper classifies Legendrian rational unknots with tight complements in certain lens spaces, providing explicit descriptions and extending the classification to specific examples like L(5,2).

Contribution

It offers the first classification of Legendrian rational unknots in lens spaces with tight complements, including explicit diagrams and examples.

Findings

Complete classification of Legendrian rational unknots in L(p,1)

Explicit contact surgery diagrams for these knots

Extension of classification to L(5,2)

Abstract

We classify Legendrian rational unknots with tight complements in the lens spaces L(p,1) up to coarse equivalence. As an example of the general case, this classification is also worked out for L(5,2). The knots are described explicitly in a contact surgery diagram of the corresponding lens space.