Contact non-squeezing in various closed prequantizations

TL;DR

This paper investigates contact non-squeezing phenomena in various closed prequantizations, introducing and computing two types of contact capacities to detect and quantify these phenomena.

Contribution

It introduces two new contact capacities based on spectral selectors, enhancing the understanding of contact non-squeezing in prequantizations.

Findings

Identification of contact non-squeezing phenomena in lens spaces and prequantizations.

Development of two contact capacities using spectral selectors.

Quantitative analysis of non-squeezing phenomena.

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.