Mathematical Sciences: "Geometry of Charateristic Classes"

数学科学：“特征类的几何”

• 批准号: 9504237
• 负责人: Dennis McLaughlin
• 金额: $ 3万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-01 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504237&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Charateristic; Classes

9504237 McLaughlin The proposed research lies in the interface of differential topology and mathematical physics. More specifically, it deals with the so called Wess-Zumino-Witten vector bundle on Teichmuller space and is an attempt to give a rigorous formula for the projectively flat connection on this bundle. In recent years several unexpected relations between topology and mathematical physics have been discovered. If completely successful, the proposed research - which is originally motivated by problems in quantum field theory - will likely shed a new light on the study of 3-dimensional spaces and knot theory.

9504237麦克劳克林提出的研究在于差异拓扑和数学物理学的界面。更具体地说，它处理了Teichmuller空间上所谓的West-Zumino-witten矢量捆绑包，并试图为该捆绑包上的投影平坦连接提供严格的公式。 近年来，已经发现了拓扑与数学物理学之间的几个意外关系。如果完全成功的话，最初是由量子场理论中的问题引起的拟议研究可能会为研究三维空间和结理论的研究提供新的启示。