Projective modules in classical and quantum functional analysis (Q847928)

This is a very well written expository article -- based on lectures given by the author at the University of Alberta in 2003 -- on the concept of a projective module in three different variants of topological homology: the ``classical'' topological homology, where the underlying tensor product is the projective Banach space tensor product, and the two ``quantized'' topological homologies, where the underlying tensor products are the projective operator space and the Haagerup tensor product, respectively.