论文标题
纤维中的线性进度
Linear progress in fibres
论文作者
论文摘要
纤维双曲线3型脉络膜从双曲机平面到双曲线3空间，纤维和歧管的各个通用盖。诱导的地图是一个嵌入，它因单个指标而呈指数扭曲。在本文中，我们开始研究沿纤维中典型射线的失真。我们验证双曲线平面中的典型射线在双曲线3空间中的环境度量中使线性进展。我们根据几何学和基本的千古理论的某些软方面来制定证明。这使我们能够将结果扩展到与封闭表面基团的某些扩展相对应的类似环境。其中包括gromov双曲线的表面组延伸，Teichmüller盘上的通用曲线以及由Birman精确序列引起的延伸。
A fibered hyperbolic 3-manifold induces a map from the hyperbolic plane to hyperbolic 3-space, the respective universal covers of the fibre and the manifold. The induced map is an embedding that is exponentially distorted in terms of the individual metrics. In this article, we begin a study of the distortion along typical rays in the fibre. We verify that a typical ray in the hyperbolic plane makes linear progress in the ambient metric in hyperbolic 3-space. We formulate the proof in terms of some soft aspects of the geometry and basic ergodic theory. This enables us to extend the result to analogous contexts that correspond to certain extensions of closed surface groups. These include surface group extensions that are Gromov hyperbolic, the universal curve over a Teichmüller disc, and the extension induced by the Birman exact sequence.
