Valentin Golodets & Vyacheslav Kulagin
Let $\R$
be an
equivalence relation generated by a countable ergodic homeomorphism
group of
a perfect Polish space $X$. We consider cocycles taking values in
Polish
groups on $\R$ modulo meager subsets of $X$. Two cocycles are called
weakly
equivalent if they are cohomologous up to an automorphism of $\R$. The
notion of generic associated Mackey action is introduced, which is an
invariant of weak equivalence for cocycles. Regular cocycles with
values in
an arbitrary Polish group and transient cocycles with values in an
arbitrary
countable group are completely classified up to weak equivalence.