Effective minimal subflows of Bernoulli flows
HTML articles powered by AMS MathViewer
- by Eli Glasner and Vladimir V. Uspenskij PDF
- Proc. Amer. Math. Soc. 137 (2009), 3147-3154 Request permission
Abstract:
We show that every infinite discrete group $G$ has an infinite minimal subflow in its Bernoulli flow $\{0,1\}^G$. A countably infinite group $G$ has an effective minimal subflow in $\{0,1\}^G$. If $G$ is countable and residually finite, then it has such a subflow which is free. We do not know whether there are groups $G$ with no free subflows in $\{0,1\}^G$.References
- Mike Boyle, Doris Fiebig, and Ulf Fiebig, Residual entropy, conditional entropy and subshift covers, Forum Math. 14 (2002), no. 5, 713–757. MR 1924775, DOI 10.1515/form.2002.031
- Alexander Dranishnikov and Viktor Schroeder, Aperiodic colorings and tilings of Coxeter groups, Groups Geom. Dyn. 1 (2007), no. 3, 311–328. MR 2314048, DOI 10.4171/GGD/15
- Robert Ellis, Universal minimal sets, Proc. Amer. Math. Soc. 11 (1960), 540–543. MR 117716, DOI 10.1090/S0002-9939-1960-0117716-1
- Eli Glasner, Ergodic theory via joinings, Mathematical Surveys and Monographs, vol. 101, American Mathematical Society, Providence, RI, 2003. MR 1958753, DOI 10.1090/surv/101
- Eli Glasner and Benjamin Weiss, Quasi-factors of zero-entropy systems, J. Amer. Math. Soc. 8 (1995), no. 3, 665–686. MR 1270579, DOI 10.1090/S0894-0347-1995-1270579-5
- E. Glasner and B. Weiss, Minimal actions of the group $\Bbb S(\Bbb Z)$ of permutations of the integers, Geom. Funct. Anal. 12 (2002), no. 5, 964–988. MR 1937832, DOI 10.1007/PL00012651
- Ilya Kapovich and Daniel T. Wise, The equivalence of some residual properties of word-hyperbolic groups, J. Algebra 223 (2000), no. 2, 562–583. MR 1735163, DOI 10.1006/jabr.1999.8104
- Vladimir Pestov, Dynamics of infinite-dimensional groups, University Lecture Series, vol. 40, American Mathematical Society, Providence, RI, 2006. The Ramsey-Dvoretzky-Milman phenomenon; Revised edition of Dynamics of infinite-dimensional groups and Ramsey-type phenomena [Inst. Mat. Pura. Apl. (IMPA), Rio de Janeiro, 2005; MR2164572]. MR 2277969, DOI 10.1090/ulect/040
- Vladimir Uspenskij, On universal minimal compact $G$-spaces, Proceedings of the 2000 Topology and Dynamics Conference (San Antonio, TX), 2000, pp. 301–308. MR 1875600
- William A. Veech, Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), no. 5, 775–830. MR 467705, DOI 10.1090/S0002-9904-1977-14319-X
Additional Information
- Eli Glasner
- Affiliation: Department of Mathematics, Tel-Aviv University, Tel Aviv, Israel
- MR Author ID: 271825
- Email: glasner@math.tau.ac.il
- Vladimir V. Uspenskij
- Affiliation: Department of Mathematics, 321 Morton Hall, Ohio University, Athens, Ohio 45701
- MR Author ID: 191555
- Email: uspensk@math.ohiou.edu
- Received by editor(s): June 19, 2007
- Received by editor(s) in revised form: December 14, 2007
- Published electronically: April 14, 2009
- Additional Notes: The first author is partially supported by BSF grant 2006119
- Communicated by: Jane M. Hawkins
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3147-3154
- MSC (2000): Primary 54H20; Secondary 20E99, 37B10
- DOI: https://doi.org/10.1090/S0002-9939-09-09905-5
- MathSciNet review: 2506474