Spectral selectors and contact orderability
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916867487039488 |
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| author | Allais, Simon Arlove, Pierre-Alexandre |
| author_facet | Allais, Simon Arlove, Pierre-Alexandre |
| contents | We study the notion of orderability of isotopy classes of Legendrian submanifolds and their universal covers, with some weaker results concerning spaces of contactomorphisms. Our main result is that orderability is equivalent to the existence of spectral selectors analogous to the spectral invariants coming from Lagrangian Floer Homology. A direct application is the existence of Reeb chords between any closed Legendrian submanifolds of a same orderable isotopy class. Other applications concern the Sandon conjecture, the Arnold chord conjecture, Legendrian interlinking, the existence of time-functions and the study of metrics due to Hofer-Chekanov-Shelukhin, Colin-Sandon, Fraser-Polterovich-Rosen and Nakamura. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10578 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral selectors and contact orderability Allais, Simon Arlove, Pierre-Alexandre Symplectic Geometry 53D35, 53D10 We study the notion of orderability of isotopy classes of Legendrian submanifolds and their universal covers, with some weaker results concerning spaces of contactomorphisms. Our main result is that orderability is equivalent to the existence of spectral selectors analogous to the spectral invariants coming from Lagrangian Floer Homology. A direct application is the existence of Reeb chords between any closed Legendrian submanifolds of a same orderable isotopy class. Other applications concern the Sandon conjecture, the Arnold chord conjecture, Legendrian interlinking, the existence of time-functions and the study of metrics due to Hofer-Chekanov-Shelukhin, Colin-Sandon, Fraser-Polterovich-Rosen and Nakamura. |
| title | Spectral selectors and contact orderability |
| topic | Symplectic Geometry 53D35, 53D10 |
| url | https://arxiv.org/abs/2309.10578 |