Contact non-squeezing in various closed prequantizations
Abstract
We describe some contact non-squeezing phenomena, first in lens spaces then in strongly order able closed prequantizations in the sense of Liu. To detect and quantify these non-squeezing phenomena we define and compute two different contact capacities. In the former case the contact capacity comes from the spectral selectors constructed by Allais, Sandon and the author by the means of generating functions and Givental's non-linear Maslov index. In the latter case the contact capacity comes from the order spectral selectors constructed by Allais and the author.
Cite
@article{arxiv.2409.10334,
title = {Contact non-squeezing in various closed prequantizations},
author = {Pierre-Alexandre Arlove},
journal= {arXiv preprint arXiv:2409.10334},
year = {2024}
}
Comments
We have replaced Proposition 6.4 (version 1) by Theorem 1.3 (version 2). The assumptions in Theorem 1.3 (version 2) are more restrictive than the ones of Proposition 6.4 (version 1), however the validity of Proposition 6.4 (version 1) was based on the validity of a conjecture while Theorem 1.3 (version 2) is fully proved by introducing a new spectral selector (section 7 of version 2)