## 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

### MSC:

 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
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### References:

 [1] Ya. M. Éliashberg, ”Rigidity of symplectic and contact structures,” Abstracts of Reports to the 7th Leningrad International Topology Conference, Leningrad (1982). [2] D. Bennequin, ”Enlancements et equations de Pfaff,” Asterisque,107–108, 97–162 (1982). [3] C. Conley and E. Zehnder, ”The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold,” Invent. Math.,73, 33–49 (1983). · Zbl 0516.58017 [4] M. Gromov, ”Pseudoholomorphic curves in symplectic manifolds,” Invent. Math.,82, 307–347 (1985). · Zbl 0592.53025 [5] J. A. Lees, ”On the classification of Lagrange immersions,” Duke Math. J.,42, No. 2, 217–224 (1976). · Zbl 0329.58006
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