Groups, Geometry, and Dynamics


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Volume 10, Issue 1, 2016, pp. 177–200
DOI: 10.4171/GGD/347

Published online: 2016-02-09

A nonamenable finitely presented group of piecewise projective homeomorphisms

Yash Lodha[1] and Justin Tatch Moore[2]

(1) Cornell University, Ithaca, USA
(2) Cornell University, Ithaca, USA

In this article we will describe a finitely presented subgroup of the group of piecewise projective homeomorphisms of the real projective line. 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 $F$.

Keywords: Amenable, finitely presented, free group, piecewise, projective, Thompson's group, torsion free

Lodha Yash, Moore Justin Tatch: A nonamenable finitely presented group of piecewise projective homeomorphisms. Groups Geom. Dyn. 10 (2016), 177-200. doi: 10.4171/GGD/347