Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-19T18:50:53.186Z Has data issue: false hasContentIssue false
  • English
  • Français

Some remarks on topological full groups of Cantor minimal systems II

Published online by Cambridge University Press:  24 July 2012

HIROKI MATUI
HIROKI MATUI*
Affiliation:
Graduate School of Science, Chiba University, Inage-ku, Chiba 263-8522, Japan (email: matui@math.s.chiba-u.ac.jp)
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that commutator subgroups of topological full groups arising from minimal subshifts have exponential growth. We also prove that the measurable full group associated to the countable, measure-preserving, ergodic and hyperfinite equivalence relation is topologically generated by two elements.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 5 , October 2013 , pp. 1542 - 1549
Copyright
Copyright © 2012 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bezuglyi, S. and Medynets, K.. Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems. Colloq. Math. 110 (2008), 409–429.Google Scholar
[2]Dahmani, F., Fujiwara, K. and Guirardel, V.. Free groups of interval exchange transformations are rare. Preprint, arXiv:1101.5909.Google Scholar
[3]Eigen, S. J.. On the simplicity of the full group of ergodic transformations. Israel J. Math. 40 (1981), 345–349.Google Scholar
[4]Giordano, T., Matui, H., Putnam, I. F. and Skau, C. F.. Orbit equivalence for Cantor minimal $\mathbb {Z}^d$-systems. Invent. Math. 179 (2010), 119–158.CrossRefGoogle Scholar
[5]Giordano, T., Putnam, I. F. and Skau, C. F.. Topological orbit equivalence and $C^*$-crossed products. J. Reine Angew. Math. 469 (1995), 51–111.Google Scholar
[6]Giordano, T., Putnam, I. F. and Skau, C. F.. Full groups of Cantor minimal systems. Israel J. Math. 111 (1999), 285–320.Google Scholar
[7]Grigorchuk, R. and Medynets, K.. Topological full groups are locally embeddable into finite groups, Preprint, arXiv:1105.0719.Google Scholar
[8]de la Harpe, P.. Topics in Geometric Group Theory (Chicago Lectures in Mathematics). University of Chicago Press, Chicago, 2000.Google Scholar
[9]Kittrell, J. and Tsankov, T.. Topological properties of full groups. Ergod. Th. & Dynam. Sys. 30 (2010), 525–545.Google Scholar
[10]Matui, H.. Some remarks on topological full groups of Cantor minimal systems. Internat. J. Math. 17 (2006), 231–251.CrossRefGoogle Scholar