Selective Floer cohomology for contact vector fields

Fuente: arXiv
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Main Authors: Cant, Dylan, Uljarević, Igor
Format: Preprint
Published: 2024
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author Cant, Dylan
Uljarević, Igor
author_facet Cant, Dylan
Uljarević, Igor
contents This paper associates a persistence module to a contact vector field $X$ on the ideal boundary of a Liouville manifold. The persistence module measures the dynamics of $X$ on the region $Ω$ where $X$ is positively transverse to the contact distribution. The colimit of the persistence module depends only on the domain $Ω$ and is a variant of the selective symplectic homology introduced by the second named author. As an application we prove existence of positive orbits for certain classes of contact vector fields. Another application of this invariant is that we recover the famous non-squeezing result of Eliashberg, Kim, and Polterovich.
format Preprint
id arxiv_https___arxiv_org_abs_2405_05443
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Selective Floer cohomology for contact vector fields
Cant, Dylan
Uljarević, Igor
Symplectic Geometry
53D40, 53D10
This paper associates a persistence module to a contact vector field $X$ on the ideal boundary of a Liouville manifold. The persistence module measures the dynamics of $X$ on the region $Ω$ where $X$ is positively transverse to the contact distribution. The colimit of the persistence module depends only on the domain $Ω$ and is a variant of the selective symplectic homology introduced by the second named author. As an application we prove existence of positive orbits for certain classes of contact vector fields. Another application of this invariant is that we recover the famous non-squeezing result of Eliashberg, Kim, and Polterovich.
title Selective Floer cohomology for contact vector fields
topic Symplectic Geometry
53D40, 53D10
url https://arxiv.org/abs/2405.05443