Appears in collection : 2021 - T2 - WS2 - Advances in symplectic topology

Joint work with Jennifer L. Dalton and John B. Etnyre.

Legendrian torus knots were classified by Etnyre and Honda. I will explain the classification of Legendrian torus links. In particular, I will describe restrictions on the Legendrian torus knots that can be realized as the components of a Legendrian torus link, and I will give examples of Legendrian torus links that cannot be destabilized even though they do not have maximal Thurston-Bennequin invariant. Furthermore, I will explain that there are some smooth symmetries of Legendrian torus links that cannot be realized by a Legendrian isotopy. These torus link statements have extensions to Legendrian cable links. All these results are applications of convex surface theory.