Bang-He Li, Tian-Jun Li
Published 2001-08-31Version 1
In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied. It is used to describe which classes in rational and irrational ruled manifolds are realized by connected symplectic surfaces. In particular, we completely determine which classes with square at least -1 in such manifolds can be represented by embedded spheres. Moreover, based on a new characterization of the action of the diffeomorphism group on the intersection forms of a rational manifold, we are able to determine the orbits of the diffeomorphism group on the set of classes represented by embedded spheres of square at least -1 in any 4-manifold admitting a symplectic structure.
Geometrically simply connected 4-manifolds and stable cohomotopy Seiberg-Witten invariants
Giroux correspondence, confoliations, and symplectic structures on S^1 x M
Boundedness of diffeomorphism groups of manifold pairs -- Circle case --
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