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Positive entropy actions of countable groups factor onto Bernoulli shifts


Author: Brandon Seward
Journal: J. Amer. Math. Soc. 33 (2020), 57-101
MSC (2010): Primary 37A35, 37A15
DOI: https://doi.org/10.1090/jams/931
Published electronically: September 27, 2019
MathSciNet review: 4066472
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Abstract: We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy), then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory.


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Additional Information

Brandon Seward
Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10003
MR Author ID: 884743
Email: b.m.seward@gmail.com

Keywords: Sinai’s factor theorem, Bernoulli shift, Rokhlin entropy, sofic entropy, non-amenable groups, completely positive entropy, Koopman representation
Received by editor(s): April 14, 2018
Received by editor(s) in revised form: April 21, 2019, and May 20, 2019
Published electronically: September 27, 2019
Additional Notes: The author was partially supported by ERC grant 306494 and Simons Foundation grant 328027 (P.I. Tim Austin).
Article copyright: © Copyright 2019 American Mathematical Society