Every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite, with the consequence that minimal crossed products are Z-stable and Elliott-classifiable.
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Elementary amenability and almost finiteness
Every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite, with the consequence that minimal crossed products are Z-stable and Elliott-classifiable.