zbMATH — the first resource for mathematics

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
[1] Ya. M. √Čliashberg, ”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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.