The Metric Aspect of Noncommutative Geometry

Abstract

Most of the previous work on ``noncommutative geometry'' could more accurately be labeled as noncommutative differential topology, in that it deals with the homology of differential forms on noncommutative spaces (cyclic homology) and vector bundles on noncommutative spaces (K-theory) [Col]. However, the essence of geometry has to do with the metric properties of spaces.