三维凸余紧$PSL_2\mathbb{C}$簇的周边双合理性
Peripheral birationality for 3-dimensional convex co-compact $PSL_2\mathbb{C}$ varieties
摘要：
设$M$是一个可双曲化的有边界$3$ -流形，$χ_0(M)$是$M$的$PSL_2\mathbb{C}$ -特征标簇的一个分支，其中包含凸余紧特征标.我们证明了$i_*:χ_0(M)\rightarrowχ(\partial M)$到$\partial M$的特征标簇的周边映射与它的象是一个双有理同构，特别是一般地是一对一映射.这推广了Dunfield（单尖双曲$3$ -流形）和Klaff-Tillmann（有限体积双曲$3$ -流形）的工作。我们使用Bonahon-Schläfli公式和离散余紧表示的体积刚性。
英文摘要：
Let $M$ be a hyperbolizable $3$-manifold with boundary, and let $χ_0(M)$ be a component of the $PSL_2\mathbb{C}$-character variety of $M$ that contains the convex co-compact characters. We show that the peripheral map $i_*:χ_0(M)\rightarrowχ(\partial M)$ to the character variety of $\partial M$ is a birational isomorphism with its image, and in particular is generically a one-to-one map. This generalizes work of Dunfield (one cusped hyperbolic $3$-manifolds) and Klaff-Tillmann (finite volume hyperbolic $3$-manifolds). We use the Bonahon-Schläfli formula and volume rigidity of discrete co-compact representations.
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