Institute of Mathematics for Industry


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Construction of minimal skew products of amenable minimal dynamical systems

Hold Date 2015-07-06 16:30~2015-07-06 18:00

Place Seminar Room 1, Institute of Mathematics for Industry, Ito Campus map, Kyushu University

Object person  

Speaker Yuhei SUZUKI (Graduate School of Mathematical Sciences, the University of Tokyo)

We give a generalization of a result of Glasner and Weiss. This provides many new examples of amenable minimal dynamical systems of exact groups. We also study the pure infiniteness of the crossed products of minimal dynamical systems arising from this result. For this purpose, we introduce and study a notion of the finite filling property for etale groupoids, which generalizes a result of Jolissaint and Robertson. As an application, we show that for any connected closed topological manifold M, every countable non-amenable exact group admits an amenable minimal free dynamical system on the product of M and the Cantor set whose crossed product is a Kirchberg algebra. This extends a result of Rørdam and Sierakowski.