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.