Abelian Livshits theorems and geometric applications
Abelian Livshits theorems and geometric applications
复制标题
DOI：
--
复制
发表时间：
2020-04
期刊：
影响因子：
--
通讯作者：
A. Gogolev;F. R. Hertz
中科院分区：
文献类型：
--
作者：
A. Gogolev;F. R. Hertz
在光滑流动中引入了阿贝尔上同的概念。这是一个比流的标准上同等价关系弱的等价关系。我们发展了传递ansov流上的阿贝尔上同的Livshits理论。特别地，我们证明了同调满Anosov流的一个阿贝尔Livshits定理。然后将该定理应用于增强负曲面的标记长度谱刚性。我们还提出了一种应用于接触阿诺索夫流的刚度。本文还给出了关于同源满Anosov流的一些新结果。
We introduce a notion of abelian cohomology in the context of smooth flows. This is an equivalence relation which is weaker than the standard cohomology equivalence relation for flows. We develop Livshits theory for abelian cohomology over transitive Anosov flows. In particular, we prove an abelian Livshits theorem for homologically full Anosov flows. Then we apply this theorem to strengthen marked length spectrum rigidity for negatively curved surfaces. We also present an application to rigidity of contact Anosov flows. Some new results on homologically full Anosov flows are also given.