8 citations · 13 across the 5 of their papers we have counts for
5 papers
-dimension groups
Thierry Giordano, Ian F. Putnam, Christian F. Skau
We study a class of simple dimension groups in which the cyclic subgroup generated by the order unit is replaced by a copy of satisfying some strict conditions. Ou…
-odometers and cohomology
Thierry Giordano, Ian F. Putnam, Christian F. SKau
Cohomology for actions of free abelian groups on the Cantor set has (when endowed with an order structure) provided a complete invariance for orbit equivalence. In this paper, we s…
Substitutional dynamical systems, Bratteli diagrams and dimension groups
Fabien Durand, Bernard Host, Christian Skau
The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithm…
The absorption theorem for affable equivalence relations
Thierry Giordano, Hiroki Matui, Ian F. Putnam +1
We prove a result about extension of a minimal AF-equivalence relation R on the Cantor set X, the extension being `small' in the sense that we modify R on a thin closed subset Y of…
Orbit equivalence for Cantor minimal Z^2-systems
Thierry Giordano, Hiroki Matui, Ian F. Putnam +1
We show that every minimal, free action of the group Z^2 on the Cantor set is orbit equivalent to an AF-relation. As a consequence, this extends the classification of minimal syste…