In this talk I will show how one constructs C*-algebras from C*-correspondences over a commutative C*-algebra C(X). A particularly tractable type of correspondence comes from the module of sections of a vector bundle where multiplication on one side of the module is given by composition by a homeomorphism α:X→X. When X is an infinite compact metric space with finite covering dimension and α is minimal, the resulting C*-algebras are classifiable by Elliott invariants. I will discuss this and related results, which is based on joint work with Adamo, Archey, Georgescu, Jeong, Strung and Viola and certain subsets thereof.

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