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The principal aim of this paper is to give a dynamical presentation of theJiang-Su algebra. Originally constructed as an inductive limit of primedimension drop algebras, the Jiang-Su algebra has gone from being a poorlyunderstood oddity to having a prominent positive role in George Elliott'sclassification programme for separable, nuclear C*-algebras. Here, we exhibitan etale equivalence relation whose groupoid C*-algebra is isomorphic to theJiang-Su algebra. The main ingredient is the construction of minimalhomeomorphisms on infinite, compact metric spaces, each having the samecohomology as a point. This construction is also of interest in dynamicalsystems. Any self-map of an infinite, compact space with the same cohomology asa point has Lefschetz number one. Thus, if such a space were also to satisfysome regularity hypothesis (which our examples do not), then the Lefschetz-HopfTheorem would imply that it does not admit a minimal homeomorphism.

Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang-Su algebra