Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the extrinsic topology of Lagrangian submanifolds   We investigate the extrinsic topology of Lagrangian submanifolds and of their
submanifolds in closed symplectic manifolds using Floer homological methods.
The first result asserts that the homology class of a displaceable monotone
Lagrangian submanifold vanishes in the homology of the ambient symplectic
manifold. Combining this with spectral invariants we provide a new mechanism
for proving Lagrangian intersection results e.g. entailing that any two simply
connected Lagrangian submanifold in $\CP^n\times\CP^n$ must intersect.

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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex