Displaying similar documents to “Secondary characteristic classes for the isotropic Grassmannian”

On implicit Lagrangian differential systems

S. Janeczko (2000)

Annales Polonici Mathematici

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Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).

Thom polynomials for open Whitney umbrellas of isotropic mappings

Toru Ohmoto (1996)

Banach Center Publications

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A smooth mapping f : L n → ( M 2 n , ω ) of a smooth n-dimensional manifold L into a smooth 2n-dimensional symplectic manifold (M,ω) is called isotropic if f*ω vanishes. In the last ten years, the local theory of singularities of isotropic mappings has been rapidly developed by Arnol’d, Givental’ and several authors, while it seems that the global theory of their singularities has not been well studied except for the work of Givental’ [G1] in the case of dimension 2 (cf. [A], [Au], [I2], [I-O]). In the present...

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

Maxim È. Kazarian (1996)

Banach Center Publications

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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].