Realisation of measured dynamics as uniquely ergodic minimal   homeomorphisms on manifolds
  We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses the following improvement of Weiss relative version of Jewett-Krieger theorem: any extension between two ergodic systems is isomorphic to a skew-product on Cantor sets. 
Fran\c{c}ois B\'eguin (LM-Orsay), Sylvain Crovisier (LAGA),   Fr\'ed\'eric Le Roux (LM-Orsay)