Groups of piecewise projective homeomorphisms

By Nicolas Monod. Proceedings of the National Academy of Sciences of the United States of America, 2012

115 citations recorded by the source corpus.

The group of piecewise projective homeomorphisms of the line provides straightforward torsion-free counterexamples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7f46859b01606639c6e107af52dde635711c686a

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Citations in the corpus

GROUP ACTIONS ON 1-MANIFOLDS: A LIST OF VERY CONCRETE OPEN QUESTIONS (2017, methodology): “Among its many remarkable properties, GLM has no free subgroup (by an easy extension of Brin-Squier’s theorem mentioned above), it is non-amenable (due to prior work of Carrière-Ghys [22] and Monod [100]), and has a finite presentation (this is the main technical contribution of [89]).”
C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-simplicity and the amenable radical (2016, unknown): “Constructions of the same flavor had already been considered at the level of the boundary: for Aut(T ) this gives rise to the notion of almost automorphism of T , and for PSL(2,R) acting on the hyperbolic disc we obtain the group of piecewise projective homeomorphisms of the circle, recently conside”
Simple groups of dynamical origin (2015, background): “There are many examples of topological full groups in this sense: the Thompson groups [4], Monod’s examples [23], a version of Lodha and Moore’s example [17], groups associated with expanding maps [25], diagram groups [9], etc.”
Extensive amenability and an application to interval exchanges (2015, background): “oup H(0)/H(2), and hence has a ﬁxed point. Such a ﬁxed point is an H(0)-invariant mean on X. The fact that H yR is not extensively amenable follows from the following Theorem because it was proved in [Mon13] that H is not amenable. Theorem 6.4. A subgroup H1 of H is amenable if and only if H1 y R is”
A nonamenable finitely presented group of piecewise projective homeomorphisms (2016, unknown): “Amenable, nitely presented, free group, piecewise, projective, ompson’s group, torsion free.”
Tensor Products of C*-Algebras and Operator Spaces (2020, background): “See Monod’s [178] for what seems to be currently the simplest construction of non-amenable groups not containing F2 as a subgroup.”