Spaces of Hyperbolic 3-Manifolds

双曲 3-流形空间

• 批准号: 0504877
• 负责人: Kenneth Bromberg
• 金额: $ 11.45万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504877&HistoricalAwards=false
• 关键词: Spaces; Hyperbolic; Manifolds

Some of the topics that will be studied include: the topology of quasiconformal deformation spaces, classification of projective structures, infinitely generated Kleinian groups and new approaches to the density conjecture for geometrically finite Kleinian groups.A 3-manifold is a mathematical object of fundamental interest. For example the space we live in is a 3-manifold. Most 3-manifolds are hyperbolic. That is they have a metric of constant curvature equal to -1. In this project the principal investigator will study 3-manifolds that carry whole families of hyperbolic metrics. These deformation spaces have an extremely complicated structure that resembles the more well known Mandelbrot set. The principal investigator will also study complex projective structures on surfaces. Projective structures are intimately related to hyperbolic 3-manifolds and results about one object often lead to results about the other.

将研究的课题包括：拟共形变形空间的拓扑、射影结构的分类、无限生成Klein群以及几何有限Klein群的密度猜想的新方法。三维流形是一个基本感兴趣的数学对象。例如，我们居住的空间是一个三维流形。大多数三维流形都是双曲线的。也就是说，它们有一个常曲率度规等于-1。在这个项目中，首席研究员将研究承载整个双曲度量族的3-流形。这些变形空间具有极其复杂的结构，类似于更广为人知的Mandelbrot集。首席研究员还将研究表面上的复杂投射结构。射影结构与双曲三维流形密切相关，关于一个对象的结果往往会导致关于另一个对象的结果。