Groups of piecewise projective homeomorphisms

Abstract

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

This version submitted to PNAS on October 22, 2012. Final version published in PNAS at http://dx.doi.org/10.1073/pnas.1218426110

References in corpus (4)

• Isometry groups of non-positively curved spaces: discrete subgroups
• The Dixmier problem, lamplighters and Burnside groups
• On the bounded cohomology of semi-simple groups, S-arithmetic groups and products
• On co-amenability for groups and von Neumann algebras

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• A computational approach to the Thompson group $F$
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• Triple transitivity and non-free actions in dimension one
• A finitely presented group of piecewise projective homeomorphisms
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• A combinatorial characterisation of amenable locally compact groups
• The ideal intersection property for essential groupoid C*-algebras
• An $n$-adic generalization of the Lodha-Moore group
• Skew-amenability of topological groups
• PL(M) admits no Polish group topology
• Equivariant measurable liftings
• Property FW and 1-dimensional piecewise groups
• Schreier graphs of actions of Thompson's group F on the unit interval and on the Cantor set
• Products of free groups in Lie groups
• Locally moving groups and laminar actions on the line
• Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature
• A note on actions with finite orbits on dendrites