Ruan, Yongbin 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) Cited in 4 Documents 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 Keywords:complex deformation; symplectic deformation; Gromov invariants PDFBibTeX XMLCite \textit{Y. Ruan}, in: Geometry and analysis on complex manifolds. Festschrift for Professor S. Kobayashi's 60th birthday. Singapore: World Scientific. 171--197 (1994; Zbl 0934.53049)