Mathematical Sciences: K-Theory, C*-algebras and Index Theory of Elliptic Operators

数学科学：K-理论、C*-代数和椭圆算子指数理论

• 批准号: 9401457
• 负责人: Jerome Kaminker
• 金额: $ 9万
• 依托单位: Indiana University
• 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: 1994-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401457&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; algebras; Index

9401457 Kaminker This project will pursue several directions involving the use of operator algebras to obtain invariants for elliptic operators, algebraic K-theory and dynamical systems. a notion of higher spectral flow will be developed. Index theoretic invariants will be defined which will detect elements of algebraic K-theory of the complex numbers. Operator algebras associated to hyperbolic dynamical systems will be studied and a K-theoretic duality relation will be used to obtain dynamical information. Work will also be done on some questions related to the Novikov conjecture and generalized homology theories on C*- algebras. These problems all involve Hilbert space operators and their relation to the geometric properties of manifolds, the higher dimensional analogues of surfaces. Partial differential operators play a large role in this work. These operators occur naturally in the study of applied mathematics and mathematical physics. ***

小行星9401457 这个项目将追求几个方向，涉及使用算子代数获得椭圆算子，代数K理论和动力系统的不变量。将发展更高频谱流的概念。指数理论的不变量将被定义，这将检测元素的代数K-理论的复数。将研究与双曲动力系统相关的算子代数，并利用K-理论对偶关系获得动力学信息。本文还将研究与Novikov猜想和C ~*-代数上的广义同调理论有关的一些问题。 这些问题都涉及希尔伯特空间算子和它们与流形的几何性质的关系，流形是曲面的高维类似物。偏微分算子在这项工作中发挥了很大的作用。这些算子在应用数学和数学物理的研究中自然出现。 ***