A nonamenable finitely presented group of piecewise projective homeomorphisms

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GROUP ACTIONS ON 1-MANIFOLDS: A LIST OF VERY CONCRETE OPEN QUESTIONS (2017, methodology): “Among the new examples of groups constructed via this approach, the most remarkable is, with no doubt, the group GLM introduced by Lodha and Moore in [89], which -as a group acting on the line- is generated by the homeomorphisms f, g, h below (notice that f, g generate a group isomorphic -actually, ”
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.”