Advanced Search

As shown by V. Vassilyev [V], $D_4^{\pm }$ singularities of arbitrary Lagrangian mappings of three-folds form no integral characteristic class. We show, nevertheless, that in the pseudooptical case the number of $D_4^{\pm }$ singularities counted with proper signs forms an invariant. We give a topological interpretation of this invariant, and its applications. The results of the paper may be considered as a 3-dimensional generalization of the results due to V. I. Arnold [A].