Spectral selectors and contact orderability

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Allais, Simon, Arlove, Pierre-Alexandre
Natura: Preprint
Pubblicazione: 2023
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866916867487039488
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