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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
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Abstract

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

Information

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

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