Conjugacy of unimodular pisot substitutions subshifts to domain   exchanges
  We prove that any unimodular Pisot substitution subshift is measurably conjugate to a domain exchange in an Euclidean space which is a finite topological extension of a translation on a torus.This generalizes the pioneer works of Rauzy and Arnoux-Ito providing geometric realizations to any unimodular Pisot substitution without any additional combinatorial condition. 
Samuel Petite (LAMFA), Fabien Durand (LAMFA)
math.DS