Minimal Cantor systems: Constraints induced by the dimension group on the (dynamical) eigenvalues

Fabien Durand (Université de Picardie Jules Verne)

Thursday 17th October 16:00-17:00 Maths 311B

Abstract

We give conditions on the subgroups of the circle to be realized as the subgroups of eigenvalues of minimal Cantor systems belonging to a determined strong orbit equivalence class that are given by means of dimension groups. Actually, the additive group of continuous eigenvalues E(X, T ) of the minimal Cantor system (X, T ) is a subgroup of the intersection I (X, T ) of all the images of the dimension group by its traces. We will present two approaches showing that the quotient group I (X, T )/E(X, T ) is torsion free. The first approach is a work of Cortez-Durand-Petite (and an extra hypothesis is needed) and the second is by Giordano-Handelman-Hosseini.

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