The program for cocycle rigidity of partially hyperbolic homgeneous abelian group actions was recently completed for irreducible models. We will discuss the geometric method for trivialization of cocycles used for the recently solved cases, and the new argument using tools from topological groups as well as new computations in group homology which played a crucial role in finishing the program. Joint work with Zhenqi Wang. Speaker(s): Kurt Vinhage (U Chicago)