Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 
 

 

Invariant random subgroups and action versus representation maximality


Authors: Peter J. Burton and Alexander S. Kechris
Journal: Proc. Amer. Math. Soc. 145 (2017), 3961-3971
MSC (2010): Primary 28D15, 37A35
DOI: https://doi.org/10.1090/proc/13591
Published electronically: April 7, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that weak containment of free ergodic measure-
preserving actions of $ \mathbb{F}_\infty $ is not equivalent to weak containment of the corresponding Koopman representations. This result is based on the construction of an invariant random subgroup of $ \mathbb{F}_\infty $ which is supported on the maximal actions.


References [Enhancements On Off] (What's this?)

  • [AE] M. Abért and G. Elek, The space of actions, partition metric and combinatorial rigidity, arXiv:1108.2147.
  • [AGV] Miklós Abért, Yair Glasner, and Bálint Virág, Kesten's theorem for invariant random subgroups, Duke Math. J. 163 (2014), no. 3, 465-488. MR 3165420, https://doi.org/10.1215/00127094-2410064
  • [BHV] Bachir Bekka, Pierre de la Harpe, and Alain Valette, Kazhdan's property (T), New Mathematical Monographs, vol. 11, Cambridge University Press, Cambridge, 2008. MR 2415834
  • [CK] Clinton T. Conley and Alexander S. Kechris, Measurable chromatic and independence numbers for ergodic graphs and group actions, Groups Geom. Dyn. 7 (2013), no. 1, 127-180. MR 3019078, https://doi.org/10.4171/GGD/179
  • [DG] A. Dudko and R. Grigorchuk, On spectra of Koopman, groupoid and quasi-regular representations, arXiv:1510.00897v2.
  • [K] Alexander S. Kechris, Global aspects of ergodic group actions, Mathematical Surveys and Monographs, vol. 160, American Mathematical Society, Providence, RI, 2010. MR 2583950
  • [K1] Alexander S. Kechris, Weak containment in the space of actions of a free group, Israel J. Math. 189 (2012), 461-507. MR 2931406, https://doi.org/10.1007/s11856-011-0182-6
  • [KT] Alexander S. Kechris and Todor Tsankov, Amenable actions and almost invariant sets, Proc. Amer. Math. Soc. 136 (2008), no. 2, 687-697 (electronic). MR 2358510, https://doi.org/10.1090/S0002-9939-07-09116-2
  • [T] Robin D. Tucker-Drob, Weak equivalence and non-classifiability of measure preserving actions, Ergodic Theory Dynam. Systems 35 (2015), no. 1, 293-336. MR 3294302, https://doi.org/10.1017/etds.2013.40

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 28D15, 37A35

Retrieve articles in all journals with MSC (2010): 28D15, 37A35


Additional Information

Peter J. Burton
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: pjburton@caltech.edu

Alexander S. Kechris
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: kechris@caltech.edu

DOI: https://doi.org/10.1090/proc/13591
Received by editor(s): August 25, 2016
Received by editor(s) in revised form: October 12, 2016
Published electronically: April 7, 2017
Additional Notes: Research partially supported by NSF Grant DMS-1464475
Communicated by: Adrian Ioana
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society