论文标题
封闭双曲线3-纤维的Menger曲线和球形CR均匀化
Menger curve and Spherical CR uniformization of a closed hyperbolic 3-orbifold
论文作者
论文摘要
令$$ g_ {6,3} = \ langle a_0，\ cdots，a_5 | a_ {i}^{3} = id，a_ {i} a_ {i+1} = a_ {i+1} a_ {i}，i \ in \ in \ mathbb {z}/6 \ mathbb {z} \ rangle $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ J. Granier \ cite {granier}构建了一个离散的，凸的和忠实的表示$ g_ {6,3} $的$ρ$ $ \ mathbf {pu}（2,1）$。我们显示，Infinity的3-孔（g_ {6,3}）$是封闭的双曲线3-孔子，其基础空间为3-Sphere和Singular locus $ \ mathbb {Z} _3 _3 $ contect occoned链链链 - 链 - 链link-link $ c（6，-2）$。这回答了Misha Kapovich的猜想10.6 \ Cite {Kapovich}的第二部分。
Let $$G_{6,3}=\langle a_0, \cdots, a_5| a_{i}^{3}=id, a_{i} a_{i+1}= a_{i+1} a_{i}, i \in \mathbb{Z}/6\mathbb{Z}\rangle$$ be a hyperbolic group with boundary the Menger curve. J. Granier \cite{Granier} constructed a discrete, convex cocompact and faithful representation $ρ$ of $G_{6,3}$ into $\mathbf{PU}(2,1)$. We show the 3-orbifold at infinity of $ρ(G_{6,3})$ is a closed hyperbolic 3-orbifold, with underlying space the 3-sphere and singular locus the $\mathbb{Z}_3$-coned chain-link $C(6,-2)$. This answers the second part of Misha Kapovich's Conjecture 10.6\cite{Kapovich}.
