具有拟Fuchsian完整性的分支投射结构
Branched projective structures with quasi-Fuchsian holonomy
摘要：
证明了：若S是具有负欧拉示性数的闭紧曲面，R是PSL（2，C）中的拟Fuchsian表示，则当k>0时，S上具有全分支阶k和完整性R的分支射影结构的变形空间M（k，R）是连通的.等价地，具有相同的拟Fuchsian完整性和相同数目的分支点的两个分支投射结构通过分支点的移动而关联。特别地，通过移动分支点获得接枝环。在附录中，我们给出了空间M（k，R）的一个显式图谱。它是一个光滑的复流形，以Hurwitz空间为模型。
英文摘要：
We prove that if S is a closed compact surface of negative Euler characteristic, and if R is a quasi-Fuchsian representation in PSL(2,C), then the deformation space M(k,R) of branched projective structures on S with total branching order k and holonomy R is connected, as soon as k>0. Equivalently, two branched projective structures with the same quasi-Fuchsian holonomy and the same number of branch points are related by a movement of branch points. In particular grafting annuli are obtained by moving branch points. In the appendix we give an explicit atlas for the space M(k,R). It is shown to be a smooth complex manifold modeled on Hurwitz spaces.
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