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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
DOI: https://doi.org/10.1090/proc/14765
Published electronically: September 20, 2019
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Abstract | References | Similar Articles | Additional Information

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?)

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Additional Information

Andy Zucker
Affiliation: Institut de Mathématiques de Jussieu - PRG, Université Paris Diderot, Paris, France 75013
Email: andrew.zucker@imj-prg.fr

DOI: https://doi.org/10.1090/proc/14765
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