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Poisson brackets of partitions of unity on surfaces

Author(s): Buhovsky, Lev; Logunov, Aleksandr; Tanny, Shira

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Abstract: Given an open cover of a closed symplectic manifold, consider all smooth partitions of unity consisting of functions supported in the covering sets. The Poisson bracket invariant of the cover measures how much the functions from such a partition of unity can become close to being Poisson commuting. We introduce a new approach to this invariant, which enables us to prove the lower bound conjectured by L. Polterovich, in dimension 2.
Publication Date: 2020
Electronic Publication Date: 16-Jun-2020
Citation: Buhovsky, Lev, Logunov, Alexander, Tanny, Shira. (2020). Poisson brackets of partitions of unity on surfaces. COMMENTARII MATHEMATICI HELVETICI, 95 (247 - 278. doi:10.4171/CMH/487
DOI: doi:10.4171/CMH/487
ISSN: 0010-2571
EISSN: 1420-8946
Pages: 247 - 278
Type of Material: Journal Article
Version: Author's manuscript

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