关于双曲平面中测得的层状结构和地震的Fréchet拓扑
A Fréchet topology on measured laminations and Earthquakes in the hyperbolic plane
摘要：
证明了有界测量层空间$ML_b(\mathbb{H})$与$λ\mapsto E^λ|_{S^1}$给出的泛Teichmüller空间$T(\mathbb{H})$之间的双射对应是$ML_b(\mathbb{H})$上的Fréchet拓扑与$T(\mathbb{H})$上的Teichmüller拓扑的同胚，其中$E^λ$是具有地震测度$λ$的地震.一个推论是离散地震测量的地震在$T(\mathbb{H})$中是密集的。我们还建立了上述结果的无穷小版本。
英文摘要：
We prove that the bijective correspondence between the space of bounded measured laminations $ML_b(\mathbb{H})$ and the universal Teichmüller space $T(\mathbb{H})$ given by $λ\mapsto E^λ|_{S^1}$ is a homeomorphism for the Fréchet topology on $ML_b(\mathbb{H})$ and the Teichmüller topology on $T(\mathbb{H})$, where $E^λ$ is an earthquake with earthquake measure $λ$. A corollary is that earthquakes with discrete earthquake measures are dense in $T(\mathbb{H})$. We also establish infinitesimal versions of the above results.
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