Poisson brackets of partitions of unity on surfaces

Lev Buhovsky; Alexander Logunov; Shira Tanny

doi:10.4171/CMH/481

Poisson brackets of partitions of unity on surfaces

Lev Buhovsky, Alexander Logunov, Shira Tanny

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	247-278
Number of pages	32
Journal	Commentarii Mathematici Helvetici
Volume	95
Issue number	1
DOIs	https://doi.org/10.4171/CMH/481
State	Published - Apr 2020

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Partition of unity
Poisson bracket invariant
Poisson non-commutativity
Symplectic surface

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10.4171/CMH/481

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AU - Logunov, Alexander

AU - Tanny, Shira

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N2 - 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.

AB - 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.

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KW - Poisson bracket invariant

KW - Poisson non-commutativity

KW - Symplectic surface

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Poisson brackets of partitions of unity on surfaces

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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