Mathematical Sciences: K-Theory and Cyclic Cohomology Related to Operator Algebras

数学科学：与算子代数相关的 K 理论和循环上同调

• 批准号: 9104513
• 负责人: Toshikazu Natsume
• 金额: $ 2.48万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104513&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Cyclic; Cohomology

Professor Natsume's project is in the area of K-theory and cyclic cohomology in noncommutative geometry. He will study operator algebras arising from geometry. Solutions to the problems he poses will illuminate the area of interaction of the two fields. Some of the specific problems he will consider are: (i) determine the structure of the group of diffeomorphisms of a twisted group C*-algebra of the fundamental group of a closed Riemann surface, (ii) determine whether the Baum-Connes conjecture is valid for codimension one foliations which are almost without holonomy, (iii) generalize the vanishing theorem of the Godbillon-Vey map in analytical K-theory to higher codimension cases, and (iv) establish a Fourier inversion formula for the canonical cyclic cocycle of a simply connected solvable Lie group. The general area of this project is operator algebras and geometry. Operators can be thought of as infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. Among other problems, Professor Natsume will study operator algebras which arise in the analysis of closed surfaces.

Natalie教授的项目是在K理论领域， 非交换几何中的循环上同调。 他将研究 由几何学产生的算子代数。 解决问题的方法 他的姿势将照亮这两个领域的相互作用。 他将考虑的一些具体问题是：（一）确定 扭群的双同态群的结构 闭黎曼曲面基本群的C *-代数， (ii)判断Baum-Connes猜想是否成立 余维一叶理，几乎没有holonomy，（iii） 推广了Godbillon-Vey映射的消失定理， 分析K-理论更高的余维情况下，和（iv）建立 的正则循环上循环的傅里叶逆公式 单连通可解李群 这个项目的一般领域是算子代数和 几何 运算符可以被认为是 复数 特殊类型的运营商经常被放在一起 在代数中，自然称为算子代数。 除其他 问题，教授Natalie将研究算子代数， 在分析封闭曲面时出现。