Mathematical Sciences: K-Theory for Amalgamated Products of C*-Algebras

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McClanahan intends to continue his study of the K-theory of operator algebras, with emphasis on those that arise as reduced C*- algebras of groups. He will use Lance's six term exact sequence of K-groups to obtain the K-groups of the reduced noncommutative unitary group C*-algebra and the reduced noncommutative Grassmanian C*-algebra. He then intends to use the techniques of Pimsner in order to generalize this exact sequence to include a certain class of full and reduced amalgamated products of C*-algebras. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These seemingly abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA.