Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak and strong fillability of higher dimensional contact manifolds   For contact manifolds in dimension three, the notions of weak and strong
symplectic fillability and tightness are all known to be inequivalent. We
extend these facts to higher dimensions: in particular, we define a natural
generalization of weak fillings and prove that it is indeed weaker (at least in
dimension five),while also being obstructed by all known manifestations of
"overtwistedness". We also find the first examples of contact manifolds in all
dimensions that are not symplectically fillable but also cannot be called
overtwisted in any reasonable sense. These depend on a higher-dimensional
analogue of Giroux torsion, which we define via the existence in all dimensions
of exact symplectic manifolds with disconnected contact boundary.

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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
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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: astro-ph