Mathematical Sciences: Two-Generator Discrete Groups: Algebra and Geometry

数学科学：二元离散群：代数和几何

• 批准号: 9001881
• 负责人: Jane Gilman
• 金额: $ 4.61万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001881&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Two; Generator; Discrete

The principal investigator will complete the study of two- generator subgroups of PSL(2,R). The investigation will result in a complete and unified account of the geometric and algebraic approaches to this classification problem, as well as a complete description of the relationship between this algebra and geometry. The investigator will also study an extension of these methods to the complex numbers and to several real variables. The work to be completed by the principal investigator has as one of its ramifications the complete understanding of tilings of the plane by tiles invariant under some sort of discrete group action. These have been of interest to mathematicians for more than a century and their study was recently revived by W. Thurston. Connections between this investigation and the topology of three dimensional hypersurfaces as well as to dynamical systems, abound.

主要研究者将完成两项研究- PSL（2，R）的生成子群。 调查将导致 在一个完整的和统一的帐户的几何和代数 解决这个分类问题的方法，以及一个完整的 这个代数和 几何研究人员还将研究这些研究的扩展 复数和多个真实的变量的方法。 主要研究者要完成的工作 作为其分支之一， 在某种离散群下不变量 行动上 数学家们对这些问题的兴趣 他们的研究已经进行了世纪，最近由W. 瑟斯顿 这次调查和 三维超曲面的拓扑以及 动力学系统，比比皆是。