The classification of Lagrangian and Legendrian singularities

The theory of generating families reduces the study of Lagrangian and Legendrian singularities to the study of singularities of families of functions and hypersurfaces. The tools developed in the preceding parts for studying the singularities of functions therefore give valuable information about caustics and fronts. In the pages which follow we give the results that have been obtained in this direction. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.