磁余切丛的辛上同调

IF 1.1 3区数学 Q1 MATHEMATICS Commentarii Mathematici Helvetici Pub Date : 2018-09-04 DOI:10.4171/cmh/555

Yoel Groman, W. Merry

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引用次数: 5

摘要

我们使用在\cite{Groman2015}中引入的紧致性耗散方法，在不限制磁形式的情况下，构造了磁余切丛的辛Floer上同调的族版本。作为一个应用，我们推导出，如果$N$是闭流形，$\sigma$是不弱精确的磁形式，那么由$\sigma确定的磁余切丛中任何紧集的$\pi_1$敏感Hofer-Zehnder容量是有限的。

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The symplectic cohomology of magnetic cotangent bundles

We construct a family version of symplectic Floer cohomology for magnetic cotangent bundles, without any restrictions on the magnetic form, using the dissipative method for compactness introduced in \cite{Groman2015}. As an application, we deduce that if $N$ is a closed manifold and $ \sigma$ is a magnetic form that is not weakly exact, then the $ \pi_1$-sensitive Hofer-Zehnder capacity of any compact set in the magnetic cotangent bundle determined by $ \sigma$ is finite.

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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.

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