Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture   We prove that any closed connected exact Lagrangian manifold L in a connected
cotangent bundle T*N is up to a finite covering space lift a homology
equivalence. We prove this by constructing a fibrant parametrized family of
ring spectra FL parametrized by the manifold N. The homology of FL will be
(twisted) symplectic cohomology of T*L. The fibrancy property will imply that
there is a Serre spectral sequence converging to the homology of FL and the
product combined with intersection product on N induces a product on this
spectral sequence. This product structure and its relation to the intersection
product on L is then used to obtain the result. Combining this result with work
of Abouzaid we arrive at the conclusion that L -> N is always a homotopy
equivalence.

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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex