论文标题
用指定的几何极限构建结
Constructing knots with specified geometric limits
论文作者
论文摘要
众所周知，任何具有无限体积的驯服双曲线3个manifold是一系列有限体积双曲结的序列的几何极限。 Purcell和Souto表明，如果原始歧管嵌入了三个角度，则可以将这种结插入3个球体中。但是，他们的证据是非建设性的。没有产生例子。在本文中，我们在几何有限的情况下给出了建设性的证明。也就是说，鉴于几何有限的是驯服双曲线3个体，一端我们建立了一个明确的结族，其补充会汇聚到几何上。我们的结位于原始歧管的（拓扑）双重。该建筑将全面增强的链接类别与克莱尼人集团设置。
It is known that any tame hyperbolic 3-manifold with infinite volume and a single end is the geometric limit of a sequence of finite volume hyperbolic knot complements. Purcell and Souto showed that if the original manifold embeds in the 3-sphere, then such knots can be taken to lie in the 3-sphere. However, their proof was nonconstructive; no examples were produced. In this paper, we give a constructive proof in the geometrically finite case. That is, given a geometrically finite, tame hyperbolic 3-manifold with one end, we build an explicit family of knots whose complements converge to it geometrically. Our knots lie in the (topological) double of the original manifold. The construction generalises the class of fully augmented links to a Kleinian groups setting.
