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An Ornstein-Weiss-Rokhlin lemma for free actions with the small boundary property

Banff International Research Station for Mathematical Innovation and Discovery

For free actions of amenable groups, we discuss an equivalent characterization of the small boundary property in terms of the existence of disjoint open towers with Folner shapes, small diameters, and the remainder having small orbit capacity. An ingredient behind this, which might be of independent interest, is a characterization of the small boundary property as having a special kind of extension on a totally disconnected space. We pose the question of whether this result can be strengthened for the remainder of the towers to be small in a stronger sense, and relate this to a desirable outcome for transformation group C*-algebras. If time permits, we may discuss actions of groups with the Tempelman condition, or possible applications for embeddings into cubical shifts. This is joint work in progress with David Kerr.

Mathematics; Dynamical systems and ergodic theory; Global analysis, analysis on manifolds; Dynamical systems

video/mp4

Author affiliation: University of Münster

2018-01-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64449

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/