Mathematical Sciences: The Mapping Class Group and the Geometry of Teichmuller Space

数学科学：映射类群和 Teichmuller 空间的几何

• 批准号: 9503449
• 负责人: Howard Masur
• 金额: $ 10.43万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503449&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Mapping; Class; Group

9503449 Masur This proposal concerns the geometry of Teichmuller space and the mapping class group. The proposer will use methods from complex geometry, probability, and dynamical systems to study Teichmuller metrics. In particular, the proposer wishes to consider random walks on Teichmuller space to study rigidity problems about the mapping class group. Teichmuller space represents the totality of pretzel-like surfaces with a fixed topological type; these surfaces, so called Riemann surfaces of a fixed genus, are crucial in the study of complex-valued functions as they generalize the complex number field. And the proposed research seeks to understand Teichmuller space from a geometric and metric point of view.

这个建议涉及到Teichmuller空间的几何和映射类群。申请者将使用复杂几何、概率和动力系统的方法来研究Teichmuller度量。特别地，我们希望考虑在Teichmuller空间上的随机漫步来研究映射类群的刚性问题。Teichmuller空间表示具有固定拓扑类型的类椒盐卷饼曲面的总体；这些曲面被称为固定属的黎曼曲面，由于它们推广了复数域，在复值函数的研究中起着至关重要的作用。本研究试图从几何和度量的角度来理解Teichmuller空间。