Groups of piecewise projective homeomorphisms

  title={Groups of piecewise projective homeomorphisms},
  author={Nicolas Monod},
I 1924, Banach and Tarski (1) accomplished a rather paradoxical feat. They proved that a solid ball can be decomposed into five pieces, which are then moved around and reassembled in such a way as to obtain two balls identical to the original one (1). This wellnigh miraculous duplication was based on Hausdorff’s (2) 1914 work. In his 1929 study of the Hausdorff–Banach–Tarski paradox, von Neumann (3) introduced the concept of amenable groups. Tarski (4, 5) readily proved that amenability is the… CONTINUE READING