Poisson Brackets of Partitions of Unity on Surfaces
Symplectic Geometry
2018-03-26 v2 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1705.02513,
title = {Poisson Brackets of Partitions of Unity on Surfaces},
author = {Lev Buhovsky and Alexander Logunov and Shira Tanny},
journal= {arXiv preprint arXiv:1705.02513},
year = {2018}
}
Comments
The results were significantly improved, the proofs were simplified