Classification of knots vs. links in contact manifolds

A contact manifold is a smooth manifold with an extra geometric structure.
A knot in a contact manifold is Legendrian if it is everywhere tangent to the contact planes. The classification problem in Legendrian knot theory is lot finer than its topological counter part. The problem gets even trickier when we start considering links. In this talk, I'll give a brief introduction to these knots and links, survey some of the important problems in this area and then discuss the classification problem for cable links of twist knots. Part of this is joint work with John Etnyre , Hyunki Min and Tom Rodewald.

No background on contact topology will be assumed.