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 covers consisting of displaceable sets in their work, we consider open covers constituting of topological disks and give a necessary and sufficient condition that Poisson bracket invariants of these covers are positive.
Citation
Kun SHI. Guangcun LU. "The Poisson Bracket Invariant for Open Covers Consisting of Topological Disks on Surfaces." Tokyo J. Math. 46 (2) 283 - 299, December 2023. https://doi.org/10.3836/tjm/1502179384
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