A theorem on the structure of wave fronts and its applications in symplectic topology. (English. Russian original) Zbl 0655.58015

Funct. Anal. Appl. 21, No. 1-3, 227-232 (1987); translation from Funkts. Anal. Prilozh. 21, No. 3, 65-72 (1987).
A combinatorial theorem on the structure of wave fronts is stated and, as its corollaries, results announced earlier in [the author, Rigidity of symplectic and contact structures, Proc. VII Intern. Topology Conf., Leningrad 1982] are proved. In particular, it is shown that the group of symplectic diffeomorphisms is \(C^ 0\)-closed in the group of all diffeomorphisms and new obstructions to the existence of symplectic and Lagrangean embeddings and Legendre isotopy are constructed.
Reviewer: S.V.Duzhin


37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58A20 Jets in global analysis
Full Text: DOI


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