Mathematical Sciences: Operator Algebras and Noncommutative Topology

本项目是关于数学理论的研究， 算子代数 关系的起点 拓扑学的这个主题是交换的 C*-代数正是那些作为以下代数出现的代数： 局部紧空间上的连续复值函数 拓扑空间(The后代数包含足够的 信息以完全恢复底层空间。 总的计划是扩展的想法和建设，从 拓扑的可交换设置到拓扑的非可交换领域 算子代数 具体的调查主题是：存在和 范畴上的同调和上同调理论的性质 C*-代数; K-理论中的环结构;上的算子域 奇异空间;和非稳定的K-理论，特别是对于简单的 C*-代数

This project is mathematical research in the theory of operator algebras. The starting point for the relationship of this subject to topology is the circumstance that the commutative C*-algebras are precisely those that arise as the algebra of continuous complex-valued functions on a locally compact topological space. (The latter algebra contains enough information to recover completely the underlying space.) The general program is to extend ideas and constructions from the commutative setting of topology to the noncommutative realm of operator algebras. Specific topics to be investigated are: existence and properties of homology and cohomology theories on the category of C*-algebras; ring structure in K-theory; operator fields over singular spaces; and nonstable K-theory, especially for simple C*-algebras.