Mathematical Sciences: K-Theory for Operator Algebras, IndexTheory, Riemann-Roch

数学科学：算子代数的 K 理论、索引理论、Riemann-Roch

• 批准号: 9102530
• 负责人: Paul Baum
• 金额: $ 14万
• 依托单位: Pennsylvania State Univ University Park
• 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 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102530&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Operator; Algebras

Baum is currently working on five projects: (1) K-homology and C*-algebra K-theory (with A. Connes). (2) Intersection theory and bivariant K-theory (with J. Block) (3) Cyclic homology and higher Riemann-Roch (with J. Block). (4) Equivariant index theory for proper actions of discrete groups (with M. Davis and C. Ogle). (5) Index theory on compact C-infinity manifolds with boundary (with R. Douglas and M. Taylor). It is hard to characterize these topics as falling within one area of mathematics. (1) combines algebraic topology and modern analysis. (2) is more algebra and algebraic geometry. (3) combines algebraic topology and algebraic geometry. (4) and (5) combine analysis and algebraic topology. To the extent that there are applications of Baum's work, they are now mostly to other parts of mathematics. It is clear that these applications are very widely distributed within mathematics, however.

Baum目前正在进行五个项目： (1)K-同调与C*-代数K-理论（A. Connes）。 (2)交理论和双变K-理论（与J. 块） (3)循环同调和更高的Riemann-Roch（与J. Block）。 (4)离散型方程真作用量的等变指标理论 组（与M. Davis和C. Ogle）。 (5)紧C-无穷流形上的指标理论 边界（与R。道格拉斯和M. Taylor）。 很难将这些主题定性为属于 数学的一个领域。 (1)结合了代数拓扑和 现代分析 (2)更多的是代数和代数几何 (3)结合了代数拓扑和代数几何。 (4)和 (5)联合收割机分析和代数拓扑学。 的程度 鲍姆的研究成果有很多应用， 数学的其他部分。 很明显，这些应用 在数学中分布非常广泛。