Lodha, Yash2019-12-222019-12-222019-12-222019-12-0110.1112/jlms.12254https://infoscience.epfl.ch/handle/20.500.14299/164156WOS:000501379600015We 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.Mathematics20f05 (primary)43a07 (secondary)diffeomorphismsintervaltext::journal::journal article::research article