Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-fillability of overtwisted contact manifolds via polyfolds   We prove that any weakly symplectically fillable contact manifold is tight.
Furthermore we verify the strong Weinstein conjecture for contact manifolds
that appear as the concave boundary of a directed symplectic cobordism whose
positive boundary satisfies the weak-filling condition and is overtwisted. The
results are obtained via polyfolds.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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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: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol