Effective classes and Lagrangian tori in symplectic four-manifolds

Jean-Yves Welschinger

Effective classes and Lagrangian tori in symplectic four-manifolds

Symplectic Geometry 2007-05-23 v1

Authors: Jean-Yves Welschinger

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

Keywords

symplectic four-manifold effective class Lagrangian torus almost complex structure holomorphic cycle

Cite

@article{arxiv.math/0701085,
  title  = {Effective classes and Lagrangian tori in symplectic four-manifolds},
  author = {Jean-Yves Welschinger},
  journal= {arXiv preprint arXiv:math/0701085},
  year   = {2007}
}

Comments

5 pages

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