Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holomorphic Curves in Blown Up Open Books   We use contact fiber sums of open book decompositions to define an infinite
hierarchy of filling obstructions for contact 3-manifolds, called planar
k-torsion for nonnegative integers k, all of which cause the contact invariant
in Embedded Contact Homology to vanish. Planar 0-torsion is equivalent to
overtwistedness, while every contact manifold with Giroux torsion also has
planar 1-torsion, and we give examples of contact manifolds that have planar
k-torsion for any $k \ge 2$ but no Giroux torsion, leading to many new examples
of nonfillable contact manifolds. We show also that the complement of the
binding of a supporting open book never has planar torsion. The technical basis
of these results is an existence and uniqueness theorem for J-holomorphic
curves with positive ends approaching the (possibly blown up) binding of an
ensemble of open book decompositions.

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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: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: cond-mat