Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contact non-squeezing at large scale in ${\mathbb R}^{2n} \times S^1$   We define a $\mathbb{Z}_k$-equivariant version of the cylindrical contact
homology used by Eliashberg-Kim-Polterovich (2006) to prove contact
non-squeezing for prequantized integer-capacity balls $B(R) \times S^1 \subset
\mathbb{R}^{2n} \times S^1$, $R \in \mathbb{N}$ and we use it to extend their
result to all $R \geq 1$. Specifically we prove if $R \geq 1$ there is no
$\psi\in \text{Cont}(\mathbb{R}^{2n} \times S^1)$, the group of compactly
supported contactomorphisms of $\mathbb{R}^{2n} \times S^1$ which squeezes
$\hat{B}(R) = B(R) \times S^1$ into itself, i.e. maps the closure of
$\hat{B}(R)$ into $\hat{B}(R)$. A sheaf theoretic proof of non-existence of
corresponding $\psi \in \text{Cont}_0(\mathbb{R}^{2n} \times S^1)$, the
identity component of $\text{Cont}(\mathbb{R}^{2n} \times S^1)$, is due to Chiu
(2014); it is not known if this is strictly weaker. Our construction has the
advantage of retaining the contact homological viewpoint of
Eliashberg-Kim-Polterovich and its potential for application in
prequantizations of other Liouville manifolds. It makes use of the
$\mathbb{Z}_k$-action generated by a vertical $1/k$-shift but can also be
related, for prequantized balls, to the $\mathbb{Z}_k$-equivariant contact
homology developed by Milin (2008) in her proof of orderability of lens spaces.

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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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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: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol