Abstract
We study minimal self-homeomorphisms of zero dimensional metrizable locally compact non-compact Hausdorff spaces. For this class of systems, we show that the ordered cohomology group is a complete invariant for strong orbit equivalence, i.e. topological orbit equivalence with continuous orbit cocycles. This is an "infinite" counterpart of a well known result of Giordano, Putnam and Skau about compact Cantor systems.
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