Livsic theorem for low-dimensional diffeomorphism cocycles
  We prove a Livsic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any dimension) which gives necessary and sufficient conditions to be a coboundary. 
Alejandro Kocsard, Rafael Potrie
math.DS math.GT