A note on minimal models for pmp actions

Zucker, Andy

doi:10.1090/proc/14765

A note on minimal models for pmp actions
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by Andy Zucker PDF

Proc. Amer. Math. Soc. 148 (2020), 1161-1168 Request permission

Abstract:

Given a countable group $G$, we say that a metrizable flow $Y$ is model-universal if by considering the various invariant measures on $Y$, we can recover every free measure-preserving $G$-system up to isomorphism. Weiss in[Dynamical systems and group actions, American Mathematical Society, Providence, RI, 2012, pp. 249–264] constructs a minimal model-universal flow. In this note, we provide a new, streamlined construction, allowing us to show that a minimal model-universal flow is far from unique.

References

G. Elek, Free minimal actions of countable groups with invariant probability measures, preprint, https://arxiv.org/abs/1805.11149.
J. Frisch, O. Tamuz, and P. Vahidi-Ferdowsi, Strong amenability and the infinite conjugacy class property, Invent. Math., to appear.
E. Glasner, T. Tsankov, B. Weiss, and A. Zucker, Bernoulli disjointness, submitted, https://arxiv.org/abs/1901.03406.
Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597, DOI 10.1007/978-1-4612-4190-4
Benjamin Weiss, Minimal models for free actions, Dynamical systems and group actions, Contemp. Math., vol. 567, Amer. Math. Soc., Providence, RI, 2012, pp. 249–264. MR 2931921, DOI 10.1090/conm/567/11253