Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-16T13:46:09.959Z Has data issue: false hasContentIssue false
  • English
  • Français

Thompson’s group $F$ is not strongly amenable

Published online by Cambridge University Press:  28 June 2017

YAIR HARTMAN ,
KATE JUSCHENKO ,
OMER TAMUZ  and
POOYA VAHIDI FERDOWSI
YAIR HARTMAN
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208, USA
KATE JUSCHENKO
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208, USA
OMER TAMUZ
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA email omertamuz@gmail.com
POOYA VAHIDI FERDOWSI
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA email omertamuz@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that Thompson’s group $F$ has a topological action on a compact metric space that is proximal and has no fixed points.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 4 , April 2019 , pp. 925 - 929
Copyright
© Cambridge University Press, 2017 

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

Aldous, D. and Lyons, R.. Processes on unimodular random networks. Electron. J. Probab. 12(54) (2007), 1454–1508.Google Scholar
Cannon, J. W. and Floyd, W. J.. What is Thompson’s group? Notices Amer. Math. Soc. 58(8) (2011), 1112–1113.Google Scholar
Cannon, J. W., Floyd, W. J. and Parry, W. R.. Notes on Richard Thompson’s groups F and T. Enseign. Math. Zbl. 42(3) (1996), 215–256.Google Scholar
Furman, A.. On minimal, strongly proximal actions of locally compact groups. Israel J. Math. 136(1) (2003), 173–187.Google Scholar
Furstenberg, H.. A Poisson formula for semi-simple Lie groups. Ann. of Math. (2) 77 (1963), 335–386.Google Scholar
Furstenberg, H.. Boundary theory and stochastic processes on homogeneous spaces. Harmonic Analysis on Homogeneous Spaces (Proceedings of Symposia Pure Mathematics, XXVI, Williams College, Williamstown, MA, 1972) . American Mathematical Society, Providence, RI, 1973, pp. 193–229.Google Scholar
Glasner, S.. Proximal Flows (Lecture Notes in Mathematics, 517) . Springer, Berlin, 1976.Google Scholar
Glasner, S.. Proximal flows of Lie groups. Israel J. Math. 45(2) (1983), 97–99.Google Scholar
Glasner, E. and Weiss, B.. Minimal actions of the group S(ℤ) of permutations of the integers. Geom. Funct. Anal. 12(5) (2002), 964–988.Google Scholar
Kaimanovich, V. A.. Thompson’s group F is not Liouville. Preprint, 2016, arXiv:1602.02971.Google Scholar