拉格朗日同位素与辛函数理论

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2016-10-30 DOI:10.4171/CMH/451

Michael Entov, Y. Ganor, Cedric Membrez

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引用次数: 5

摘要

研究了辛流形中拉格朗日子流形的两个相关不变量。对于拉格朗日环面，这些不变量是环面第一上同调上的函数。第一个不变量具有拓扑性质，与给定拉格朗日通量的拉格朗日同位素研究有关。更具体地说，它测量了第一上同调中直线路径的长度，可以用拉格朗日同位素的拉格朗日通量来实现。第二个不变量是解析性质的，来自辛函数理论。它被定义为允许在圆上振动的拉格朗日子流形，并具有动力学解释。我们对某些拉格朗日环面部分地计算了这些不变量。

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Lagrangian isotopies and symplectic function theory

We study two related invariants of Lagrangian submanifolds in symplectic manifolds. For a Lagrangian torus these invariants are functions on the first cohomology of the torus. The first invariant is of topological nature and is related to the study of Lagrangian isotopies with a given Lagrangian flux. More specifically, it measures the length of straight paths in the first cohomology that can be realized as the Lagrangian flux of a Lagrangian isotopy. The second invariant is of analytical nature and comes from symplectic function theory. It is defined for Lagrangian submanifolds admitting fibrations over a circle and has a dynamical interpretation. We partially compute these invariants for certain Lagrangian tori.

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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.