Mathematical Sciences: Topology, Geometry and Arithmetic

数学科学：拓扑、几何和算术

• 批准号: 9108050
• 负责人: Walter Neumann
• 金额: $ 14.34万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-15 至 1994-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9108050&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topology; Geometry; Arithmetic

Walter Neumann will continue his study (previously supported by DMS-8805551) of the topology of complex curves and surfaces and their singularities and of the geometry and arithmetic of low-dimensional manifolds. Alan Reid will study arithmetic and geometric aspects of hyperbolic 3-manifolds, with special emphasis on questions of existence of incompressible surfaces, isospectrality, special arithmetic and geometric properties of knot complements, and the Lehmer conjecture. Low-dimensional manifolds are very natural geometric objects and deserve to be thoroughly understood. The physical world is a 3-dimensional or 4-dimensional manifold, depending upon whether one includes the time dimension. Hyperbolic metrics are in some ways more natural than Euclidean metrics, even through locally our world appears to be Euclidean.

沃尔特·诺依曼将继续他的研究（以前 DMS-8805551支持）的复杂曲线的拓扑结构， 曲面及其奇点和几何形状， 低维流形的算术 艾伦·里德将学习数学和几何方面的知识， 双曲3-流形，特别强调的问题， 不可压缩曲面的存在性，等谱性，特殊性 结补数的算术和几何性质，以及 Lehmer猜想 低维流形是非常自然的几何对象 值得被彻底理解 物理世界是一个 3-二维或四维流形，取决于是否 一个包括时间维度。 双曲度量在一些 比欧几里德度量更自然的方式，即使通过局部 我们的世界似乎是欧几里得的。