ABSTRACT
The theory of Legendrian knots first introduced by Dmitry Fuchs and Serge Tabachnikov [FT], lies at the juncture of knot theory, the theory of wave fronts and contact geometry.
Legendrian knots in R3 represent the one-dimensional case of Legendrian manifolds (in the general case, a Legendrian manifold is a k-dimensional submanifold in a (2k+ 1)–dimensional manifold satisfying some conditions). The Legendrian knot theory is interesting because it allows us to introduce a new equivalence for knots: besides topological isotopy, one can consider an isotopy in the space of Legendrian knots.
