Two new families of finitely generated simple groups of homeomorphisms of the real line
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The goal of this article is to exhibit two new families of finitely generated simple groups of homeomorphisms of R. These families are strikingly different from existing families owing to the nature of their actions on R, and exhibit surprising algebraic and dynamical features. The first construction provides the first examples of finitely generated simple groups of homeomorphisms of R that also admit minimal actions by homeomorphisms on the torus. The second construction provides the first examples of finitely generated simple groups of homeomorphisms of R which also admit a minimal action by homeomorphisms on the circle. This also provides new examples of finitely generated simple groups that admit nontrivial homogeneous quasimorphisms (and therefore have infinite commutator width), also being the first such left orderable examples.
|Tidsskrift||Journal of Algebra|
|Status||Udgivet - 1 dec. 2023|
During this research Yash Lodha was supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1301-51 and by a KIAS Individual Grant at the Korea Institute for Advanced Study , and an FWF START project at the University of Vienna ( Y-1411 ). Yash Lodha is currently partially supported by an NSF CAREER grant 2240136 . Cristóbal Rivas was partially supported by FONDECYT 1181548 .
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