Baum-Connes conjecture and expanders (C03)

Baum-Connes 猜想和扩展器 (C03)

• 批准号: 179733397
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/179733397?language=en
• 关键词: Baum; Connes; conjecture; expanders; C03

We study C*-algebras constructed from locally compact (semi)groups or group actions, by means of topological invariants such as their K-theory groups. One major tool for this is given by (confirmed cases of) the Baum-Connes conjecture. Known counterexamples to the Baum-Connes conjecture involve groups (Gromov's monster groups) that admit coarse embeddings of expanders. We will study a new formulation of the conjecture that avoids the existing counterexamples, and we will study the relation between the coarse geometry of expanders and rigidity properties for groups and operator algebras.

我们研究了由局部紧（半）群或群作用构造的C*-代数，借助于拓扑不变量，如它们的K-理论群。一个主要的工具，这是由（证实的情况下）鲍姆-康纳斯猜想。已知的鲍姆-康纳斯猜想的反例涉及允许扩张子粗嵌入的群（格罗莫夫的怪物群）。我们将研究一个新的配方的猜想，避免现有的反例，我们将研究之间的关系，粗几何的扩张和刚性性质的群体和算子代数。