Transverse-Legendrian links

In recent joint works of the present author with M. Prasolov and V. Shastin a new technique for distinguishing Legendrian knots has been developed. In this paper the technique is extended further to provide a tool for distinguishing transverse knots. It is shown that the equivalence problem for transverse knots with trivial orientation-preserving symmetry group is algorithmically solvable. In a future paper the triviality condition for the orientation-preserving symmetry group will be dropped.