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