尺寸为$\geq 7的动态奇异接触球体$

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2017-06-20 DOI:10.4171/cmh/468

Marcelo R. R. Alves, Matthias Meiwes

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引用次数: 12

摘要

我们展示了$S^{2n-1}$上的接触结构的第一个例子，其中$n\geq4$和$S^3\timesS^2$，它们都配备了它们的标准光滑结构，其中每个Reeb流都具有正拓扑熵。作为研究Reeb流体积增长的一种新的技术工具，我们引入了包裹Floer同调的代数增长的概念。它的力量来源于它在刘域上的几个几何运算下的稳定性。

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Dynamically exotic contact spheres in dimensions $\geq 7$

We exhibit the first examples of contact structures on $S^{2n-1}$ with $n\geq 4$ and on $S^3\times S^2$, all equipped with their standard smooth structures, for which every Reeb flow has positive topological entropy. As a new technical tool for the study of the volume growth of Reeb flows we introduce the notion of algebraic growth of wrapped Floer homology. Its power stems from its stability under several geometric operations on Liouville domains.

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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.