A finitely presented group of piecewise projective homeomorphisms

Abstract

In this article we will describe a finitely presented subgroup of Monod's group of piecewise projective homeomorphisms of R. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. It is in fact the first such example which is torsion free. We will also develop a means for representing the elements of the group by labeled tree diagrams in a manner which closely parallels Richard Thompson's group F.

Formerly "A geometric solution to the von Neumann-Day problem for finitely presented groups". Section added on tree diagrams. Minor revisions elsewhere

References in corpus (1)

• Groups of piecewise projective homeomorphisms

Cited by in corpus (1)

• A nonamenable type $F_{\infty }$ group of piecewise projective homeomorphisms