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A note on minimal models for pmp actions

Author: Andy Zucker
Journal: Proc. Amer. Math. Soc. 148 (2020), 1161-1168
MSC (2010): Primary 37B05; Secondary 28D15
Published electronically: September 20, 2019
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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 [Enhancements On Off] (What's this?)

  • [1] G. Elek, Free minimal actions of countable groups with invariant probability measures, preprint,
  • [2] J. Frisch, O. Tamuz, and P. Vahidi-Ferdowsi, Strong amenability and the infinite conjugacy class property, Invent. Math., to appear.
  • [3] E. Glasner, T. Tsankov, B. Weiss, and A. Zucker, Bernoulli disjointness, submitted,
  • [4] Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597
  • [5] 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,

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Additional Information

Andy Zucker
Affiliation: Institut de Mathématiques de Jussieu - PRG, Université Paris Diderot, Paris, France 75013

Received by editor(s): March 19, 2019
Received by editor(s) in revised form: July 11, 2019
Published electronically: September 20, 2019
Additional Notes: The author was supported by NSF Grant no. DMS 1803489.
Communicated by: Nimish Shah
Article copyright: © Copyright 2019 American Mathematical Society