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

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00121976
Contributor : Jean-Yves Welschinger Connect in order to contact the contributor
Submitted on : Friday, December 22, 2006 - 7:46:57 PM
Last modification on : Monday, December 7, 2020 - 3:00:03 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 8:35:08 PM

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### Citation

Jean-yves Welschinger. Effective classes and Lagrangian tori in symplectic four-manifolds. J. Symplectic Geom., 2007, 5 (1), pp.9-18. ⟨10.4310/JSG.2007.v5.n1.a3⟩. ⟨ensl-00121976⟩

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