Causal hierarchy of spacetimes, temporal functions and smoothness of   Geroch's splitting. A revision
  After the heroic epoch of Causality Theory, problems concerning the smoothability of time functions and Cauchy hypersurfaces remained as unanswered folk questions. Just recently solved, our aim is to discuss the state of the art on this topic, including self-contained proofs for questions on causally continuous, stably causal and globally hyperbolic spacetimes. 
Miguel S\'anchez