论文标题
Abelian Livshits定理和几何应用
Abelian Livshits theorems and geometric applications
论文作者
论文摘要
我们在平滑流动的背景下介绍了阿贝利亚的共同体概念。这是一个等价关系，比流量的标准共同体等效关系弱。我们开发了阿贝尔共同体学理论，而不是瞬态的Anosov流。特别是，我们证明了Abelian Livshits定理，用于同源性全Anosov流动。然后，我们将此定理应用于负弯曲表面的标记长度刚度。我们还提出了接触Anosov流的刚性的应用。还给出了一些关于同源性完整Anosov流量的新结果。
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.
