交换Livshits定理及其几何应用
Abelian Livshits theorems and geometric applications
摘要：
在光滑流的背景下，我们引入了阿贝尔上同调的概念。这是一个比流的标准上同调等价关系弱的等价关系。我们发展了传递Anosov流上交换上同调的Livshits理论。特别地，我们证明了一个阿贝尔Livshits定理同调满Anosov流。然后将该定理应用于加强负曲面的显长谱刚性。我们还提出了一个应用程序的刚性接触Anosov流。给出了同调满Anosov流的一些新结果。
英文摘要：
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.
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