Legendrian framings for two-bridge links

TL;DR

This paper characterizes the Thurston-Bennequin polytope for two-bridge links and constructs non-quasipositive surfaces with quasipositive sub-annuli, advancing understanding in Legendrian link theory.

Contribution

It provides a complete description of the Thurston-Bennequin polytope for two-bridge links and constructs new examples of non-quasipositive surfaces.

Findings

Thurston-Bennequin polytope for two-bridge links is explicitly described.

Constructed non-quasipositive surfaces with all sub-annuli quasipositive.

Enhanced understanding of Legendrian framings and surface properties.

Abstract

We define the Thurston-Bennequin polytope of a two-component link as the convex hull of all pairs of integers that arise as framings of a Legendrian representative. The main result of this paper is a description of the Thurston-Bennequin polytope for two-bridge links. As an application, we construct non-quasipositive surfaces in $\R^3$ all whose sub-annuli are quasipositive.