Invariants of Legendrian links

Abstract

We introduce new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is the powerful Chekanov-Eliashberg differential graded algebra, which we reformulate and generalize. We give applications to Legendrian knots and links in three-space and in the solid torus. A related question, the calculation of the maximal Thurston-Bennequin number for a link, is answered for some large classes of links.