Polynomial growth, comparison, and the small boundary property
Dynamical Systems
2021-11-29 v3 Operator Algebras
Abstract
We show that a minimal action of a finitely generated group of polynomial growth on a compact metrizable space has comparison. It follows that if such an action has the small boundary property then it is almost finite and its -crossed product is -stable, and consequently that such crossed products are classified by their Elliott invariant.
Cite
@article{arxiv.2108.04670,
title = {Polynomial growth, comparison, and the small boundary property},
author = {Petr Naryshkin},
journal= {arXiv preprint arXiv:2108.04670},
year = {2021}
}
Comments
2nd version: fixed mistakes in the proofs; added Lemma 3.1. 3rd version: added an acknowledgement