Mathematical Sciences: Operator Algebras and Noncommutative Topology

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94013162 Blackadar The investigator proposes to continue work on a range of problems concerning the structure of operator algebras and noncommutative algebraic topology. Specific topics to be studied are: structure of inductive limits of C*-algebras, structure of groupoids and their C*-algebras, nonstable K-theory and the fundamental comparability question, and existence and properties of cohomology theories on C*-algebras. The proposed work will lead toward a description of the internal structure of a class of algebras which arise naturally throughout mathematics and mathematical physics. It has become very important to understand these algebras, and most of the necessary tools now seem to have been developed, by the proposer and others, to lead us to believe a complete description is within reach. ***