Abstract
In this paper, we show that, without involving theC*-bundle theory, elementary differential topology can do the classification of homogeneousC*-crossed productC(X) xαZ, whereX is a compact differentiable manifold of low dimension and α is a diffeomorphism ofX. The motivation of this work is the Shultz's theorem which states that aC*-algebra can be identified with its pure state space carryingw*-topology and certain geometric structure.
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