Effective classes and Lagrangian tori in symplectic four-manifolds

Abstract

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 $H_2(X;\mathbb{Z})$.

5 pages