ИСТИНА

By a transverse-Legendrian knot I call a knot which is transverse with respect to the standard contact structure on the three-sphere and Legendrian with respect to the mirror image of the standard contact structure. There is a natural combinatorial way to represent such knots so that each isotopy class admits only finitely many presentations, which can be easily searched. So the problem of comparing transverse-Legendrian knots viewed up to isotopy (within the class of transverse-Legendrian knots) has a simple algorithmic solution. Combined with our recent joint results with M.Prasolov and V.Shastin, this allows one to distinguish transverse knots in many cases when the known transverse knot invariants fail to do so.