Orderability, contact non-squeezing, and Rabinowitz Floer homology

• Verfasst von: Albers, Peter [VerfasserIn]
• Verfasst von: Merry, Will J. [VerfasserIn]
• Titel: Orderability, contact non-squeezing, and Rabinowitz Floer homology
• Verf.angabe: Peter Albers, Will J. Merry
• Jahr: 2018
• Umfang: 67 S.
• Fussnoten: Doi funktioniert nicht ; Gesehen am 01.07.2019
• Titel Quelle: Enthalten in: The journal of symplectic geometry
• Ort Quelle: [Somerville, Mass.] : Internat. Press, 2001
• Jahr Quelle: 2018
• Band/Heft Quelle: 16(2018), 6, Seite 1481-1547
• ISSN Quelle: 1540-2347
• DOI: doi:10.4310/JSG.2018.v16.n6.a1
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Mathematics - Dynamical Systems
• Sach-SW: Mathematics - Symplectic Geometry
• K10plus-PPN: 166813389X

Abstract

We study Liouville fillable contact manifolds $(\Sigma,\xi)$ with non-zero 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. This can be used to prove a general non-squeezing result, which amongst other examples in particular recovers the beautiful non-squeezing results from [EKP06].