Legendrian Torus and Cable Links

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. I will also describe how these torus link statements have extensions to Legendrian cable links. These results are applications of convex surface theory. This is joint work with Jennifer L. Dalton and John B. Etnyre.