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Umbilical characteristic number of Lagrangian mappings of 3-dimensional pseudooptical manifolds

Maxim È. Kazarian — 1996

Banach Center Publications

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].

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