论文标题
Veech组的扩展I：双曲线作用
Extensions of Veech groups I: A hyperbolic action
论文作者
论文摘要
鉴于在封闭表面$ s $的映射类组中的一个格子小组，本文研究了$γ$的几何形状，即相关的$π_1S$ - 扩展组。我们证明$γ$是捆绑几何形状的基本捆绑组的基本组。我们的主要结果是，通用覆盖物的“明显”产品区域崩溃会产生$γ$在双曲线空间上的作用，从而保留了$γ$的大部分几何形状。该动作是续集中的关键要素，在该续集中，我们表明$γ$在层次上是双曲线和准静态刚性的。
Given a lattice Veech group in the mapping class group of a closed surface $S$, this paper investigates the geometry of $Γ$, the associated $π_1S$--extension group. We prove that $Γ$ is the fundamental group of a bundle with a singular Euclidean-by-hyperbolic geometry. Our main result is that collapsing "obvious" product regions of the universal cover produces an action of $Γ$ on a hyperbolic space, retaining most of the geometry of $Γ$. This action is a key ingredient in the sequel where we show that $Γ$ is hierarchically hyperbolic and quasi-isometrically rigid.
