Two new families of finitely generated simple groups of homeomorphisms of the real line
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Two new families of finitely generated simple groups of homeomorphisms of the real line. / Hyde, James; Lodha, Yash; Rivas, Cristóbal.
In: Journal of Algebra, Vol. 635, 2023, p. 1-22.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Two new families of finitely generated simple groups of homeomorphisms of the real line
AU - Hyde, James
AU - Lodha, Yash
AU - Rivas, Cristóbal
N1 - Publisher Copyright: © 2023 Elsevier Inc.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Finitely generated group
KW - Left orderable groups
KW - Simple groups
U2 - 10.1016/j.jalgebra.2023.07.020
DO - 10.1016/j.jalgebra.2023.07.020
M3 - Journal article
AN - SCOPUS:85167430216
VL - 635
SP - 1
EP - 22
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -
ID: 371203513