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Liouville polarizations and the rigidity of their Lagrangian skeleta in dimension 4

2024/07/12 by Emmanuel Opshtein, Opshtein, Emmanuel, Felix Schlenk +1 · 1 citation
Mathematics · #53D05 #53D10 #53D12 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2407.09408

openalex publication_date 2024/07/12 · openalex created_date 2024/07/16 · openalex updated_date 2026/07/28

Abstract

The main theme of this paper is the introduction of a new type of polarizations, suited for some open symplectic manifolds, and their applications. These applications include symplectic embedding results that answer a question by Sackel-Song-Varolgunes-Zhu and Brendel, new Lagrangian non-removable intersections at small scales, and a novel phenomenon of Legendrian barriers in contact geometry.

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