Mathematical Sciences: Low Dimensional Topology

数学科学：低维拓扑

• 批准号: 9208054
• 负责人: Michael Freedman
• 金额: $ 21.77万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208054&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Low; Dimensional; Topology

Freedman has recently been concerned with applications of topology to other areas of mathematics, including geometry, ideal MHD, and signal processing, as well as continuing his program in four-dimensional manifold theory. Thurston's geometrization conjecture is the most interesting problem in the latter area, and the analytic tools for studying it, such as Hamilton's equation, may now be available. With the addition of a time dimension, the world we live in is a four-dimensional manifold, which makes it that much more intriguing that dimension four is where various anomalies in manifold theory occur. Freedman was one of the prime movers in discovering these. For example, in all other dimensions there is only one differentiable structure on n-space, i.e. one way of doing calculus, but in dimension four this is known not to be the case.

弗里德曼最近一直关注的应用程序， 拓扑学到其他数学领域，包括几何学、理想 MHD，和信号处理，以及继续他的计划， 四维流形理论 瑟斯顿几何化 猜想是最有趣的问题，在后者的领域，和 研究它的分析工具，如汉密尔顿方程， 现在可以使用。 随着时间维度的增加，我们生活的世界 一个四维流形，这使得它 有趣的是，第四维度是各种异常的地方， 多个理论出现。 弗里德曼是1949年 发现这些。 例如，在所有其他维度中， 在n-空间上只有一个可微结构，即一种方法 微积分，但在第四维中，这是已知的不是这种情况。