Selective Floer cohomology for contact vector fields

2024/05/08 by Dylan Cant, Cant, Dylan, Igor Uljarević +1 · 1 citation
Engineering · Mathematics · #53D10 #53D40 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2405.05443

openalex publication_date 2024/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• A survey on orderability and contact non-squeezing

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