论文标题
三维凸面共同处理$ psl_2 \ mathbb {c} $品种的外围异常性
Peripheral birationality for 3-dimensional convex co-compact $PSL_2\mathbb{C}$ varieties
论文作者
论文摘要
令$ m $成为带边界的夸张$ 3 $ - manifold，而让$χ_0（m）$为$ psl_2 \ mathbb {c} $的组成部分 - 字符变体$ m $，包含convex co compompact字符。我们表明，向外围地图$ i _*：χ_0（m）\rightArrowχ（\ partial m）$ to $ \ partial m $的字符品种是具有其图像的生育同构，尤其是一对一的映射。这概括了Dunfield（一个尖锐的双曲线$ 3 $ -Manifolds）和Klaff-Tillmann（有限的柔双曲线$ 3 $ -Manifolds）的工作。我们使用bonahon-schläfli公式和离散共同表征的体积刚度。
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.
