Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Torsion in Contact Manifolds   We extract a nonnegative integer-valued invariant, which we call the "order
of algebraic torsion", from the Symplectic Field Theory of a closed contact
manifold, and show that its finiteness gives obstructions to the existence of
symplectic fillings and exact symplectic cobordisms. A contact manifold has
algebraic torsion of order zero if and only if it is algebraically overtwisted
(i.e. has trivial contact homology), and any contact 3-manifold with positive
Giroux torsion has algebraic torsion of order one (though the converse is not
true). We also construct examples for each nonnegative k of contact 3-manifolds
that have algebraic torsion of order k but not k - 1, and derive consequences
for contact surgeries on such manifolds. The appendix by Michael Hutchings
gives an alternative proof of our cobordism obstructions in dimension three
using a refinement of the contact invariant in Embedded Contact Homology.

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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom