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Symplectomorphism groups and almost complex structures
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This paper studies groups of symplectomorphisms of ruled surfaces for symplectic forms with varying cohomology class. This class is characterized by the ratio R of the size of the base to that of the fiber. By considering appropriate spaces of almost complex structures, we investigate how the topological type of these groups changes as R increases. If the base is a sphere, this changes precisely when R passes an integer, and for general bases it stabilizes as R goes to infinity. Our results extend and make more precise some of the conclusions of Abreu--McDuff concerning the rational homotopy type of these groups for rational ruled surfaces.
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Cited by 2 Pith papers
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Family Seiberg-Witten equation on Kahler surface and $\pi_i(\Symp)$ on multiple-point blow ups of Calabi-Yau surfaces
Infinite generation of some higher homotopy groups of symplectomorphism groups is proved for n-point Kahler blowups of tori, K3 surfaces, and Enriques surfaces with non-resonant Kahler classes.
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