ИСТИНА

The talk is based on a joint work with Maxim Prasolov. We have shown recently that any isotopy class of a Giroux's convex surface can be presented by what we call a rectangular diagram of a surface. This applies simultaniously to two contact structures in the three-sphere, the standard one and its mirror image. We show that Giroux's convexity classes of a surface with respect to these contact structures are in a sense independent. This allows us to prove that certain isotopy classes of curves on a Seifert surface of a given Legendrian knot cannot be realized as a dividing set of a convex surface. If they are realized for another Legendrian knot having the same topological type, we can conclude that the Legendrian types of the knots are distinct.