Mathematical Sciences: Studies in Non-Commutative Geometry

数学科学：非交换几何研究

• 批准号: 9401192
• 负责人: Henri Moscovici
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401192&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Non; Commutative

9401192 Moscovici The proposed research aims to: (1) develop an Alexander-Spanier version of the Chern character; (2) obtain explicit local formulae for the Pontryagin classes of topological manifolds; (3) develop a theory of straight characteristic classes for foliations of Lipschitz manifolds; (4) obtain residual index formulae for abstract elliptic operators in terms of the Dixmier trace; (5) recover the holomorphic torsion of a Hermitian locally symmetric manifold by means of a geometric zeta function. The "quantized" differential and integral calculus, recently invented by Alain Connes, will be applied to the treatment of certain open problems in several areas of mathematics -topology, geometry and operator algebras. ***

提出的研究目标是：(1)开发一个亚历山大-西班牙语版本的陈氏字符；(2)得到拓扑流形的Pontryagin类的显式局部公式；(3)建立了Lipschitz流形叶化的直特征类理论；(4)利用Dixmier迹得到抽象椭圆算子的残差指标公式；(5)利用几何zeta函数恢复厄米局部对称流形的全纯扭转。“量子化”的微分和积分微积分，最近由阿兰·科恩斯发明，将被应用于处理若干数学领域的某些开放问题——拓扑学、几何和算子代数。* * *