Finitely presented groups with infinitely many non-homeomorphic   asymptotic cones
  We construct a finitely presented group with infinitely many non-homeomorphic asymptotic cones. We also show that the existence of cut points in asymptotic cones of finitely presented groups does, in general, depend on the choice of scaling constants and ultrafilters. 
Denis Osin, Abderezak Ould Houcine
math.GR math.GT