Umbilical characteristic number of Lagrangian mappings of 3-dimensional pseudooptical manifolds
Volume 33 / 1996
Banach Center Publications 33 (1996), 161-170
DOI: 10.4064/-33-1-161-170
Abstract
As shown by V. Vassilyev [V], $D_4^±$ singularities of arbitrary Lagrangian mappings of three-folds form no integral characteristic class. We show, nevertheless, that in the pseudooptical case the number of $D_4^±$ 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].
