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
Additional Information
- Andy Zucker
- Affiliation: Institut de Mathématiques de Jussieu - PRG, Université Paris Diderot, Paris, France 75013
- MR Author ID: 1064415
- Email: andrew.zucker@imj-prg.fr
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1161-1168
- MSC (2010): Primary 37B05; Secondary 28D15
- DOI: https://doi.org/10.1090/proc/14765
- MathSciNet review: 4055943