Contact non-squeezing and orderability via the shape invariant

TL;DR

This paper establishes a contact non-squeezing theorem for certain embeddings in contact geometry, demonstrating non-triviality of contactomorphisms and utilizing the shape invariant to prove orderability.

Contribution

It introduces a new contact non-squeezing result for starshaped domains, providing a novel proof of orderability via the shape invariant.

Findings

Proves contact non-squeezing for specific embeddings

Shows absence of positive loops of contactomorphisms

Uses shape invariant to establish orderability

Abstract

We prove a contact non-squeezing result for a class of embeddings between starshaped domains in the contactization of the symplectization of the unit cotangent bundle of certain manifolds. The class of embeddings includes embeddings which are not isotopic to the identity. This yields a new proof that there is no positive loop of contactomorphisms in the unit cotangent bundles under consideration. The proof uses the shape invariant introduced by Sikorav and Eliashberg.