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.

Freedman最近一直关注拓扑在其他数学领域的应用，包括几何，理想MHD和信号处理，以及在四维流形理论中继续他的程序。 Thurston的几何化猜想是后一个领域中最有趣的问题，现在可以使用用于研究它的分析工具，例如汉密尔顿方程。 随着时间维度的增加，我们生活的世界是一个四维的多种流形，这使得尺寸四的动物更加有趣，即歧管理论中各种异常发生的地方。 弗里德曼（Freedman）是发现这些的主要推动者之一。 例如，在所有其他维度中，n空间上只有一个可区分的结构，即一种进行微积分的方法，但是在维度四，这并非如此。