Geodesic
A nonamenable finitely presented group of piecewise projective homeomorphisms
Yash Lodha1 ; Justin Tatch Moore1 orcid
1Cornell University, Ithaca, USA
Groups, geometry, and dynamics, Tome 10 (2016) no. 1, pp. 177-200

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DOI

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.
DOI : 10.4171/ggd/347
Classification : 43-XX, 20-XX
Mots-clés : Amenable, finitely presented, free group, piecewise, projective, Thompson's group, torsion free

Yash Lodha  1   ; Justin Tatch Moore  1

1 Cornell University, Ithaca, USA 
Yash Lodha; Justin Tatch Moore. A nonamenable finitely presented group of piecewise projective homeomorphisms. Groups, geometry, and dynamics, Tome 10 (2016) no. 1, pp. 177-200. doi: 10.4171/ggd/347
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     title = {A nonamenable finitely presented group of piecewise projective homeomorphisms},
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     pages = {177--200},
     year = {2016},
     volume = {10},
     number = {1},
     doi = {10.4171/ggd/347},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/347/}
}
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