Orderability, contact non-squeezing, and Rabinowitz Floer homology (Q668763)

From the author's summary: We study Liouville fillable contact manifolds \((\Sigma,\xi)\) with non-zero and spectrally finite Rabinowitz Floer homology and assign spectral numbers to paths of contactomorphisms. As a consequence we prove that \(\widetilde{\mathrm{Cont}_0}(\Sigma,\xi)\) is orderable in the sense of Eliashberg and Polterovich. This provides a new class of orderable contact manifolds. If the contact manifold is in addition periodic or a prequantization space \(M \times S^1\) for \(M\) a Liouville manifold, then we construct a contact capacity in the sense of Sandon. This can be used to prove a general non-squeezing result, which amongst other examples in particular recovers the beautiful non-squeezing results from the paper [Geom. Topol. 10, 1635--1748 (2006; Zbl 1134.53044)] of \textit{Y. Eliashberg} et al.