The first cohomology of the mapping class group with coefficients in   algebraic functions on the SL(2, C) moduli space
  Consider a compact surface of genus at least two. We prove that the first cohomology group of the mapping class group with coefficients in the space of algebraic functions on the SL(2, C) moduli space vanishes. 
J{\o}rgen Ellegaard Andersen, Rasmus Villemoes