The first Johnson subgroups act ergodically on SU_2-character varieties
  We show that the first Johnson subgroup of the mapping class group of a surface S of genus greater than one acts ergodically on the moduli space of representations of the fundamental group of S in SU_2. Our proof relies on a local description of the latter space around the trivial representation and on the Taylor expansion of trace functions. 
Louis Funar, Julien March\'e
math.GT math.DS