Orderability, contact non-squeezing, and Rabinowitz Floer homology
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 provi...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2018
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| In: |
The journal of symplectic geometry
Year: 2018, Jahrgang: 16, Heft: 6, Pages: 1481-1547 |
| ISSN: | 1540-2347 |
| Online-Zugang: | Resolving-System, Volltext: https://dx.doi/10.4310/JSG.2018.v16.n6.a1
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| Verfasserangaben: | Peter Albers, Will J. Merry |
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| 520 | |a 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]. | ||
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