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Using SFT techniques, Eliashberg, Kim and Polterovich (2006) proved that if$\pi R_2^2 \leq K \leq \pi R_1^2$ for some integer $K$ then there is no contactsqueezing in $\mathbb{R}^{2n} \times S^1$ of the prequantization of the ball ofradius $R_1$ into the prequantization of the ball of radius $R_2$. This resultwas extended to the case of balls of radius $R_1$ and $R_2$ with $1 \leq \piR_2^2 \leq \pi R_1^2$ by Chiu (2017) and the first author (2016), usingrespectively microlocal sheaves and SFT. In the present article we recover thisgeneral contact non-squeezing theorem using generating functions, a classicalmethod based on finite dimensional Morse theory. More precisely, we develop anequivariant version, with respect to a certain action of a finite cyclic group,of the generating function homology for domains of $\mathbb{R}^{2n} \times S^1$defined by the second author (2011). A key role in the construction is playedby translated chains of contactomorphisms, a generalization of translatedpoints.

Contact non-squeezing at large scale via generating functions