Abstract

We construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold, compute some associated arithmetic invariants and exhibit the skinning map along the deformation locus. The key idea is to construct a one-dimensional family of hyperbolic polyhedra; reflections in some of the faces of the polyhedra then generate a family of Kleinian groups.

中文翻译：

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Quasifuchsian边界的非圆柱双曲3-流形的构造

摘要

我们构造了一个非圆柱双曲 3 流形的一维（实）变形，计算了一些相关的算术不变量，并展示了沿变形轨迹的蒙皮图。关键思想是构造一维双曲多面体族；多面体的一些面的反射然后产生一个克莱因群族。