Symplectic genus, minimal genus and diffeomorphisms

Details Symplectic genus, minimal genus and diffeomorphisms Symplectic genus, minimal genus and diffeomorphisms

2001-08-31

arxiv.org/abs/math/0108227v1

Mathematics

Geometric Topology

28 pages

Scientific paper

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.

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