Mathematical Sciences: Geometry and Topology of 3-Dimensional Manifolds

数学科学：三维流形的几何和拓扑

• 批准号: 9024796
• 负责人: Joel Hass
• 金额: $ 5.4万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9024796&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Topology; Dimensional

This project is concerned with problems in 3-dimensional manifold theory through the application and extension of differential geometric methods. It aims to explore the classification of non-Haken 3-manifolds and their diffeomorphisms, Heegaard splittings of 3-manifolds and universal coverings of 3- manifolds. The plan is to use the theory of minimal surfaces and of flows and evolution equations to study these problems. Three- dimensional manifolds are very natural objects of study, inasmuch as the space we live in (ignoring time) has three dimensions, but a surprising amount remains to be learned about them.

该项目关注三维问题 流形理论通过应用和扩展 微分几何方法 它旨在探讨 非Haken三维流形的分类及其超同态， 三维流形的Heegaard分裂与三维流形的万有覆盖 流形 该计划是使用最小曲面理论， 和演化方程来研究这些问题。 三个-- 维流形是非常自然的研究对象，因为 因为我们生活的空间（忽略时间）有三个维度， 关于它们，还有大量的知识有待了解。