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Symplectic topology and complex surfaces. (English) Zbl 0934.53049

Mabuchi, T. (ed.) et al., Geometry and analysis on complex manifolds. Festschrift for Professor S. Kobayashi’s 60th birthday. Singapore: World Scientific. 171-197 (1994).
The article deals with deformation equivalence of smooth complex surfaces. Symplectic deformation equivalence is compared with complex deformation equivalence. For complex surfaces of even Betti numbers, the complex deformation equivalence is shown to imply symplectic equivalence. This result allows to apply symplectic methods to problems of complex surfaces. The existence of “Gromov invariants” for higher genus pseudoholomorphic curves is shown. These are applied to obtain results on elliptic surfaces and their diffeomorphism group.
For the entire collection see [Zbl 0867.00037].
Reviewer: C.Günther (Libby)

MSC:

53D05 Symplectic manifolds (general theory)
58D27 Moduli problems for differential geometric structures
53C55 Global differential geometry of Hermitian and Kählerian manifolds
57R17 Symplectic and contact topology in high or arbitrary dimension
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