Two new families of finitely generated simple groups of homeomorphisms of the real line

Research output: Contribution to journal › Journal article › Research › peer-review

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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

Harvard

Hyde, J, Lodha, Y & Rivas, C 2023, 'Two new families of finitely generated simple groups of homeomorphisms of the real line', Journal of Algebra, vol. 635, pp. 1-22. https://doi.org/10.1016/j.jalgebra.2023.07.020

APA

Hyde, J., Lodha, Y., & Rivas, C. (2023). Two new families of finitely generated simple groups of homeomorphisms of the real line. Journal of Algebra, 635, 1-22. https://doi.org/10.1016/j.jalgebra.2023.07.020

Vancouver

Hyde J, Lodha Y, Rivas C. Two new families of finitely generated simple groups of homeomorphisms of the real line. Journal of Algebra. 2023;635:1-22. https://doi.org/10.1016/j.jalgebra.2023.07.020

Author

Hyde, James ; Lodha, Yash ; Rivas, Cristóbal. / Two new families of finitely generated simple groups of homeomorphisms of the real line. In: Journal of Algebra. 2023 ; Vol. 635. pp. 1-22.

Bibtex

@article{ec227bbf4b4a4b3f98a98ffe7defbce3,
title = "Two new families of finitely generated simple groups of homeomorphisms of the real line",
abstract = "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.",
keywords = "Finitely generated group, Left orderable groups, Simple groups",
author = "James Hyde and Yash Lodha and Crist{\'o}bal Rivas",
note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",
year = "2023",
doi = "10.1016/j.jalgebra.2023.07.020",
language = "English",
volume = "635",
pages = "1--22",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press",

}

RIS

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