复射影结构与Schottky完整性的嫁接
Some Graftings of Complex Projective Structures with Schottky Holonomy
摘要：
设$\mathcal{G}^*(S,ρ)$是一个图，它的顶点是具有完整性$ρ$的复投射结构，它的边是从一个顶点到另一个顶点的嫁接.如果$ρ$是拟Fuchsian的，则Goldman的定理暗示$\mathcal{G}^*(S,ρ)$是连通的。如果$ρ(π_1(S))$是一个肖特基群，巴巴已经证明了$\mathcal{G}(S,ρ)$（对应于未标记结构的图）是连通的。对于$ρ(π_1(S))$是Schottky基团的情况，本文给出了在基本情况下的接枝组成公式。使用这些公式，人们可以构建无限数量的（标准）投射结构，这些结构可以嫁接到一个公共结构上。此外，人们可以构造成对的投射结构，它们可以通过无数种方式嫁接连接。
英文摘要：
Let $\mathcal{G}^*(S,ρ)$ be the graph whose vertices are marked complex projective structures with holonomy $ρ$ and whose edges are graftings from one vertex to another. If $ρ$ is quasi-Fuchsian, a theorem of Goldman implies that $\mathcal{G}^*(S,ρ)$ is connected. If $ρ(π_1(S))$ is a Schottky group Baba has shown that $\mathcal{G}(S,ρ)$ (the corresponding graph for unmarked structures) is connected. For the case that $ρ(π_1(S))$ is a Schottky group, this paper provides formulae for the composition of graftings in a basic setting. Using these formulae, one can construct an infinite number of (standard) projective structures which can be grafted to a common structure. Furthermore, one can construct pairs of projective structures which can be connected by grafting in an infinite number of ways.
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