Reparamétrisation universelle d'une famille de cycles : une nouvelle approche des relations d'équivalence méromorphe. (Universal reparametrization of a family of cycles: a new approach about meromorphic equivalence relations) (Q1572647)

If \(Z\) is a reduced complex analytic space of finite dimension, the author investigates the structure of all closed \(n\)-cycles of \(Z\) trying to introduce a finite dimensional analytic structure on some nice subsets of this space. Such a subset may be the set of cycles described by an analytic family of \(n\)-cycles parametrized by a weakly normal space \(S\) and, as the structure should not depend on the parametrizing space \(S\), the author is brought to the study of a problem of universal reparametrization. The meromorphic families of \(n\)-cycles of \(Z\) and a universal reparametrization problem in this context are also studied.