On Thurston’s Parameterization of CP1-Structures
On Thurston’s Parameterization of CP1-Structures
复制标题
关于 Thurston CP1 结构的参数化
DOI：
10.1007/978-3-030-55928-1_6
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Shinpei Baba
中科院分区：
文献类型：
--
作者：
Shinpei Baba
Thurston在双曲空间中建立了-结构（复射影结构）与等变褶曲面的对应关系，给出了-结构变形空间的参数化。在本文中，我们在[15]和[17]的基础上总结了Thurston的-结构参数化，给出了其构造的概要和要点，并利用参数化给出的褶皱曲面对以下著名的-结构定理给出了独立的证明。(1)关于具有拟Fuchsian完整性的结构的戈德曼定理。(2)中不连续域上发展映射的路径提升性质。
Thurston established a correspondence between-structures (complex projective structures) and equivariant pleated surfaces in the hyperbolic-three space, in order to give a parameterization of the deformation space of-structures. In this note, we summarize Thurston’s parametrization of-structures, based on [15] and [17], giving an outline and the key points of its construction.In addition we give independent proofs for the following well-known theorems on-structures by means of pleated surfaces given by the parameterization. (1) Goldman’s Theorem on-structures with quasi-Fuchsian holonomy. (2) The path lifting property of developing maps in the domain of discontinuities in.