Spherical CR uniformization of Dehn surgeries of the Whitehead link complement

IF 2 1区 数学
M. Acosta
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引用次数: 13

Abstract

We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the complex hyperbolic plane $\mathbb{H}^2_{\mathbb{C}}$. We deform the Ford domain of Parker and Will in $\mathbb{H}^2_{\mathbb{C}}$ in a one parameter family. On the one side, we obtain infinitely many spherical CR uniformizations on a particular Dehn surgery on one of the cusps of the Whitehead link complement. On the other side, we obtain spherical CR uniformizations for infinitely many Dehn surgeries on the same cusp of the Whitehead link complement. These manifolds are parametrized by an integer $n \geq 4$, and the spherical CR structure obtained for $n = 4$ is the Deraux-Falbel spherical CR uniformization of the Figure Eight knot complement.
Whitehead节补体Dehn手术的球形CR均匀化
为了得到携带球形CR结构的Whitehead连杆补的无穷多个Dehn算子,我们应用了球面CR - Dehn算子定理。我们以Parker和Will在复双曲平面上使用Ford定域构造的Whitehead连杆补的球面CR均匀化为出发点 $\mathbb{H}^2_{\mathbb{C}}$. 我们改变帕克和威尔的福特域 $\mathbb{H}^2_{\mathbb{C}}$ 在一个参数族中。一方面,我们在Whitehead连杆补的一个顶点上得到了一个特定的Dehn手术上的无穷多个球面CR均匀化。另一方面,在Whitehead连杆补的同一尖端上,我们得到了无限多个Dehn手术的球面CR均匀化。这些流形由一个整数参数化 $n \geq 4$,得到球形CR结构 $n = 4$ 是德劳-法贝尔球形CR均匀化的8字形结补。
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来源期刊
Geometry & Topology
Geometry & Topology 数学-数学
自引率
5.00%
发文量
34
期刊介绍: Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.
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