Non-amenable groups without free subgroups
Mark Sapir of Vanderbilt University
We give a finitely presented counterexample to the von Neumann
conjecture: a
finitely presented non-amenable group without non-cyclic free
subgroups. Our
group is torsion-by-cyclic and satisfies the law [x,y]^n=1. This
answers
questions by Grigorchuk, Cohen, Gromov and others.
The paper involved, Publ. IHES (96,2002), can be obtained at
www.math.vanderbilt.edu/~msapir/publications.html"