表面上统一分区的泊松括号

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2020-06-16 DOI:10.4171/cmh/487

Lev Buhovsky, Alexander Logunov, Shira Tanny

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引用次数: 11

摘要

给定一个闭辛流形的开覆盖，考虑由覆盖集中支持的函数组成的所有光滑的统一划分。盖上的泊松括号不变量测量了从这样一个单位分割得到的函数有多少可以接近泊松交换。我们引入了一种新的方法来解决这个不变量，它使我们能够证明L. Polterovich猜想的下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Poisson brackets of partitions of unity on surfaces

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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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.