Some applications of groups of essential values of cocycles in topological dynamics

Abstract

A class of examples showing that a measure-theoretical characterization of regular cocycles in terms of essential values is not valid in topological dynamics is constructed. An example that in topological dynamics for the case of non-abelian groups, the groups of essential values of cohomologous cocycles need not be conjugate is given. A class of base preserving equivariant isomorphisms of Rokhlin cocycle extensions of topologically transitive flows is described. In particular, the topological centralizer of Rokhlin cocycle extension of minimal rotation defined by an action of the group $\mathbb R^m$ is determined.