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Symplectic topology, holomorphic convexity and contact structures [after Y. Eliashberg, D. McDuff et al.]. (Topologie symplectique, convexité holomorphe et structures de contact [d’après Y. Eliashberg, D. McDuff et al.].) (French) Zbl 0755.32009
Sémin. Bourbaki, Vol. 1989/90, 42ème année, Astérisque 189-190, Exp. No. 725, 285-323 (1990).
This work is a survey on some papers of Y. Eliashberg, D. McDuff, A. Floer, M. Gromov et al. The first section looks over Stein manifolds and contact manifolds. There are presented without proof some recent results of Eliashberg. The second section entitled “Symplectic Fillings” gives some results of M. Gromov [Invent. Math. 82, 307–347 (1985; Zbl 0592.53025)], D. McDuff, A. Floer and Y. Eliashberg (preprints, Berkeley, 1988). The section three presents two conjectures on complex surfaces, being formulated for projective planes by R. Thom. One can see the history and the references for both conjectures. The second conjecture has been proved by Eliashberg. The main results of the section are due to Eliashberg, D. McDuff, Dedford, Donaldson and Klingenberg. The fourth section contains some comments and examples concerning “Points complex and holomorphic disks”. The holomorphic hull of real surfaces is considered in the fifth section and related to this the main result is a theorem of Eliashberg. The sixth section is consecrated to the Riemann-Hilbert problem. The paper ends with some problems about the applications of Complex Analysis in Symplectic Topology. We hint at a very rich and up to date bibliography.
[For the entire collection see Zbl 0722.00001.]

MSC:
32C99 Analytic spaces
32E10 Stein spaces, Stein manifolds
53D05 Symplectic manifolds, general
53D10 Contact manifolds, general
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