This research project concerns noncommutative differential geometry and topology. This project deals with developing special functors that have been discovered by the principal investigator. These functors are used to study systematically the dense subalgebras of certain algebras that arise in modern analysis. These dense subalgebras carry more sensitive geometric data in many areas of application. Previously known algebraic K- theory and cyclic theory functors are sensitive to this data but tend to be uncomputable. The principal investigator's functors are designed to provide better access to geometric information about these dense subalgebras. The project is in the general area of analysis and geometry. It concerns the study of certain 'mappings', which are called functors. These functors determine invariants of the topology and geometry of certain manifolds significant to the geometric aspects of the mathematical sciences.
