The Poisson bracket invariant for open covers consisting of topological disks on surfaces

2019/05/20 by K. Shi, Guangcun Lu, Shi, Kun +1
Engineering · Mathematics · #53D50 #57K20 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1905.07939

openalex publication_date 2019/05/20 · openalex created_date 2023/03/23 · openalex updated_date 2026/07/28

Abstract

L. Buhovsky, A. Logunov and S. Tanny proved the (strong) Poisson bracket conjecture by Leonid Polterovich in dimension 2. In this note, instead of open cover consisting of displaceable sets in their work, we consider open cover constituted of topological discs and give a necessary and sufficient condition that Poisson bracket invariants of these covers are positive.

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