Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective classes and Lagrangian tori in symplectic four-manifolds   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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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int