Plane curves, wavefronts and Legendrian knots

Abstract

We survey some of the recent results on Legendrian knots and links in the standard contact 3–space and solid torus. These include the description of finite–order invariants and estimates of the self–linking number coming from the classical polynomial link invariants. We also describe the combinatorial invariant introduced by Chekanov and Pushkar, which allowed them to prove Arnold's conjecture on the necessity of four–cusp curves in generic eversions of a circular front in the plane.