扭曲Rabinowitz-Floer同调的第一步

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry Pub Date : 2021-05-28 DOI:10.4310/JSG.2023.v21.n1.a3

Yannis Bahni

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引用次数: 1

摘要

Rabinowitz-Floer同源性是指与Kai Cieliebak和Urs Frauenfelder于2009年提出的Rabinowitz动作泛函相关的flower意义上的Morse-Bott同源性。在我们的工作中，我们考虑将这个理论推广到一个Liouville自同构的Rabinowitz-Floer同调。作为一个应用，我们证明了对称星形超曲面商上不可收缩周期Reeb轨道的存在性。我们的理论特别适用于镜头空间。

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First steps in twisted Rabinowitz–Floer homology

Rabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer associated with the Rabinowitz action functional introduced by Kai Cieliebak and Urs Frauenfelder in 2009. In our work, we consider a generalisation of this theory to a Rabinowitz-Floer homology of a Liouville automorphism. As an application, we show the existence of noncontractible periodic Reeb orbits on quotients of symmetric star-shaped hypersurfaces. In particular, our theory applies to lens spaces.

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来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.