Geometric limits of knot complements

被引：9

作者：

Purcell, Jessica S. ^{[1
]}

Souto, Juan ^{[2
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

JOURNAL OF TOPOLOGY | 2010年 / 3卷 / 04期

基金：

美国国家科学基金会;

关键词：

HYPERBOLIC; 3-MANIFOLDS; KLEINIAN-GROUPS; MANIFOLDS; CONVERGENCE; BOUNDARIES; CORES;

D O I：

10.1112/jtopol/jtq020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that any complete hyperbolic 3-manifold with finitely generated fundamental group, with a single topological end, and which embeds into S-3 is the geometric limit of a sequence of hyperbolic knot complements in S-3. In particular, we derive the existence of hyperbolic knot complements that contain balls of arbitrarily large radius. We also show that a complete hyperbolic 3-manifold with two convex cocompact ends cannot be a geometric limit of knot complements in S-3.

引用

页码：759 / 785

页数：27

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