Contact Homology, Capacity and Non-Squeezing in R^2n x S^1 via Generating Functions

TL;DR

This paper extends symplectic capacity concepts to contact geometry, providing new proofs of non-squeezing phenomena in higher-dimensional contact manifolds using generating functions.

Contribution

It introduces a contact version of Viterbo capacity and symplectic homology, expanding tools for contact topology analysis.

Findings

Established a contact analogue of Viterbo capacity

Provided a new proof of the non-squeezing theorem in contact settings

Extended symplectic homology constructions to contact manifolds

Abstract

Starting from the work of Bhupal, we extend to the contact case the Viterbo capacity and Traynor's construction of symplectic homology. As an application we get a new proof of the Non-Squeezing Theorem of Eliashberg, Kim and Polterovich.