CAREER: Geometry of Groups and the Novikov Conjecture

职业：群几何和诺维科夫猜想

• 批准号: 0349367
• 负责人: Erik Guentner
• 金额: $ 40.99万
• 依托单位: University of Hawaii
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0349367&HistoricalAwards=false
• 关键词: CAREER; Geometry; Groups; Novikov; Conjecture

The Novikov higher signature conjecture, a deep problem in the topology of manifolds, follows from a sufficiently precise understanding of the K-theory of the unitary dual, viewed as a noncommutative space, of the group in question. This project focuses on issues related to this conjecture, in particular (1) approximation properties of group C*-algebras, (2) uniform embeddability of discrete groups in Hilbert space and (3) the use of controlled methods to study the K-theory of group C*-algebras. The investigator will also study parallel problems for C*-algebras associated to metric spaces.In studying the noncommutative dual spaces of discrete groups, with particular emphasis on the important Novikov and Baum-Connes conjectures, this project fits squarely within Alain Connes' program of noncommutative geometry. A recurring theme will be to incorporate a greater variety of ideas from geometric group theory into the study of analytic properties of groups. Indeed, the project will provide a forum for promoting sustained interaction between researchers in noncommutative geometry and geometric group theory.

诺维科夫更高的签名猜想是多种多样拓扑中的一个深层问题，遵循了对统一双重二元理论的足够精确的理解，被视为所讨论的小组的非共同空间。 该项目侧重于与该猜想有关的问题，特别是（1）组C* - 代数的近似属性，（2）希尔伯特空间中离散组的均匀嵌入性，以及（3）使用受控方法研究C*-ergebras组的K理论。 研究人员还将研究与公制空间相关的C* - 代数的并行问题。在研究离散群体的非交流性双空间，特别强调了重要的Novikov和Baum-Connes猜想，该项目在Alain Connes的非交换性质量图中完全拟合。 反复出现的主题将是将几何群体理论的更多思想纳入组的分析特性研究。 实际上，该项目将为促进研究人员在非交流性几何学和几何群体理论中持续相互作用提供一个论坛。