Mathematical Sciences: Operator Algebras and Noncommutative Topology

该项目是算子代数理论的数学研究。 该主题与拓扑关系的出发点是这样的情况：可交换的 C* 代数正是作为局部紧拓扑空间上的连续复值函数的代数而出现的代数。 （后一个代数包含足够的信息来完全恢复底层空间。）一般程序是将思想和构造从拓扑的交换设置扩展到算子代数的非交换领域。 需要研究的具体主题是：C*-代数范畴上同调和上同调理论的存在性和性质； K理论中的环结构；奇异空间上的运算符域；和不稳定的 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.