Ordered cohomology:orbit equivalence, flow equivalence and solenoids
by
Mike Boyle
University of Maryland
Coauthors: David Handelman

Ordered cohomology:orbit equivalence, flow equivalence and solenoids Let Y be the mapping torus derived from a homeomorphism T of a compact zero dimensional metrizable space X. So, the first Cech cohomology of Y is isomorphic to the group C(X, Z)/(I-T)C(X, Z). With positive set C(X, Z_+)/(I-T)C(X, Z), this becomes a unital preordered group. The order structure gives significant extra invariants of the topological space Y and the dynamical system T. There is a remarkable theory in the minimal case, due to Giordano-Putnam-Skau; beyond other results there is a rich frontier with striking open questions. I'll give a survey including some joint work with David Handelman.

Date received: February 13, 1998