Bounded orbit injections and flow equivalence for minimal Z^d actions.
by
Nicholas Ormes
University of Denver
Coauthors: Sam Lightwood

Let T and S be two minimal Z^d actions of the Cantor set. In this talk, we will discuss the relationship of (1) the existence of a certain kind of orbit preserving map (a bounded orbit injection) from T to S and (2) the existence of homeomorphism between the suspension spaces of T and S (flow equivalence). We show that as in the d=1 case, these notions are essentially equivalent. In particular we show that (1) implies (2) and if T and S are flow equivalent then there are bounded orbit injections from both T and S into a common minimal action R. Further, we use an order structure on the dth Cech cohomology groups of the suspension spaces to isolate some cases in which we can take R to be T or S. The result is a "restricted orbit equivalence" description of flow equivalence analogous to the way del Junco and Rudolph characterize Kakutani equivalence for ergodic Z^d actions.

Date received: February 26, 2003