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- W2218868493 abstract "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 $psiin text{Cont}(mathbb{R}^{2n} times S^1)$, 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." @default.
- W2218868493 created "2016-06-24" @default.
- W2218868493 creator A5068740847 @default.
- W2218868493 date "2015-12-30" @default.
- W2218868493 modified "2023-09-27" @default.
- W2218868493 title "Contact non-squeezing at large scale in ${mathbb R}^{2n} times S^1$" @default.
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