Poisson brackets of partitions of unity on surfaces

Lev Buhovsky, Alexander Logunov, Shira Tanny

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 languageEnglish (US)
Pages (from-to)247-278
Number of pages32
JournalCommentarii Mathematici Helvetici
Issue number1
StatePublished - Apr 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics


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


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