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research article
A finitely presented infinite simple group of homeomorphisms of the circle
December 1, 2019
We construct a finitely presented, infinite, simple group that acts by homeomorphisms on the circle, but does not admit a non-trivial action by C1-diffeomorphisms on the circle. This is the first such example. The group emerges as a group of piecewise projective homeomorphisms of S1=R?{infinity}. We also show that it does not admit a non-trivial action by piecewise linear homeomorphisms of the circle. Another interesting and new feature of this example is that it produces a non-amenable orbit equivalence relation with respect to the Lebesgue measure.
Use this identifier to reference this record
Type
research article
Web of Science ID
WOS:000501379600015
Authors
Publication date
2019-12-01
Publisher
Volume
100
Issue
3
Start page
1034
End page
1064
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
December 22, 2019