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.