Effective classes and Lagrangian tori in symplectic four-manifolds

Details Effective classes and Lagrangian tori in symplectic four-manifolds Effective classes and Lagrangian tori in symplectic four-manifolds

2007-01-03

arxiv.org/abs/math/0701085v1

Mathematics

Symplectic Geometry

5 pages

Scientific paper

An effective class in a closed symplectic four-manifold $(X, \omega)$ is a
two-dimensional homology class which is realized by a $J$-holomorphic cycle for
every tamed almost complex structure $J$. We prove that effective classes are
orthogonal to Lagrangian tori in $H_2 (X ; \Bbb{Z})$.

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