Boundary amenability of groups via ultrapowers
  We use $\mathrm{C}^{\ast}$-algebra ultrapowers to give a new construction of the Stone-Cech compactification of a separable, locally compact space. We use this construction to give a new proof of the fact that groups that act isometrically, properly, and transitively on trees are boundary amenable. 
Stephen Avsec and Isaac Goldbring
math.GR math.GN math.OA