Smooth cocycles rigidity for lattice actions (Q1902228)

In order to calculate cocycles of group actions, the author gives a new duality method. By using this method several results concerning trivializations of cocycles for some classes of subgroup actions on groups are obtained. After that, a rigidity theorem for the \(C^\infty\) (real) cocycles of actions of cocompact lattices \(\Gamma\) in semi-simple connected Lie groups \(G\) on a class of homogeneous spaces (in fact, on \(N \backslash G\), for a class of closed subgroups \(N\) of \(G)\) is shown: under some conditions one has \(H (\Gamma, N \backslash G) = H(G,N \backslash G)\), where \(H(G,X)\), \(G\) a group acting on a space \(X\), denotes the set of equivalence classes of cocycles.