Orbit equivalence,flow equivalence and ordered cohomology |
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Authors: | Mike Boyle David Handelman |
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Institution: | (1) Department of Mathematics, University of Maryland, 20742 College Park, MD, USA;(2) Mathematics Department, University of Ottawa, K1N 6N5 Ottawa, Ontario, Canada |
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Abstract: | We study self-homeomorphisms of zero dimensional metrizable compact Hausdorff spaces by means of the ordered first cohomology
group, particularly in the light of the recent work of Giordano Putnam, and Skau on minimal homeomorphisms. We show that flow
equivalence of systems is analogous to Morita equivalence between algebras, and this is reflected in the ordered cohomology
group. We show that the ordered cohomology group is a complete invariant for flow equivalence between irreducible shifts of
finite type; it follows that orbit equivalence implies flow equivalence for this class of systems. The cohomology group is
the (pre-ordered) Grothendieck group of the C*-algebra crossed product, and we can decide when the pre-ordering is an ordering, in terms of dynamical properties. |
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Keywords: | |
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