Mathematical Sciences: Research in Index Foliation Theory

数学科学：指数叶理理论研究

• 批准号: 9504084
• 负责人: Franz Kamber
• 金额: $ 9万
• 依托单位: University of Illinois at Urbana-Champaign
• 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: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504084&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Index; Foliation

9504084 Kamber The proposed research is in index and foliation theory with applications to mathematical physics. The proposed problems are central problems in the abstract index theory and have significant applications to gauge theories and anomalies. Foliation reduction techniques introduced earlier by the investigator may prove to have interesting connections to the newly discovered Seiberg-Witten monopole equations. Foliation theory seeks to understand the global behavior of spaces of solutions to ordinary differential equations; index theory assigns integers and other easily identifiable quantities to these spaces and aims to distinguish different spaces by means of their indices. The techniques and results developed here continue to find applications in various parts of mathematical physics.

小行星9504084 拟议的研究是在指数和叶理理论与数学物理的应用。所提出的问题是抽象指标理论中的核心问题，对度量理论和异常有重要的应用。研究者早先介绍的叶简化技术可能被证明与新发现的Seiberg-Witten方程有有趣的联系。 叶状理论寻求理解常微分方程解空间的全局行为;指数理论将整数和其他易于识别的量分配给这些空间，并旨在通过其指数来区分不同的空间。这里开发的技术和结果继续在数学物理的各个部分找到应用。