Flow Equivalence for Dynamical Systems and the Corresponding C*-Algebras

Abstract

The purpose of this paper is to describe a method of using flow equivalence for homeomorphisms to construct certain projections in the corresponding transformation group C*-algebras, by following a program which was outlined in our recent paper [15]. Using methods stemming from work of Connes [3] and Rieffel and Green [21] we will explicitly construct the strong Morita equivalence bimodule relating two C -algebras associated to flow equivalent transformations, and the corresponding projections; these projections will be related to the isomorphism of Connes between KO(C*(Y,Z)) and K1(M(Y)) where (Y,Z) is a dynamical system, C*(Y,Z) the associated C*-algebra, and M(Y) is the mapping torus for (Y.Z).