teichmller空间上的交点数和一些度量

Pub Date : 2020-01-01 DOI:10.18910/73741

Zongliang Sun, Hui Guo

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引用次数: 0

摘要

设T (X)为g属≥2的封闭曲面X的teichm ller空间，C(X)为X上测地线电流的空间，L: T (X)→C(X)为Bonahon引入的将双曲度规映射到相应的刘维尔电流的嵌入。本文分别比较了交点数与T (X)上的teichm ller度量、长度谱度量和Thurston不对称度量之间的定量关系和拓扑行为。

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Intersection number and some metrics on Teichmüller space

Let T (X) be the Teichmüller space of a closed surface X of genus g ≥ 2, C(X) be the space of geodesic currents on X, and L : T (X)→ C(X) be the embedding introduced by Bonahon which maps a hyperbolic metric to its corresponding Liouville current. In this paper, we compare some quantitative relations and topological behaviors between the intersection number and the Teichmüller metric, the length spectrum metric and Thurston’s asymmetric metrics on T (X), respectively.

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