On the topology of a complex-analytic normalization

In this paper the problem of constructing a normalization of a complex-analytic space is considered. The transition from a complex space to its normalization is carried out in two stages: in the first stage only the topology of the original space is changed; in the second stage “completion” of the structure sheaf takes place without change in the topology. The first stage is studied in detail; it is shown that an operation can be defined on the class of all pseudomanifolds which, applied to the body of the simplicial complex triangulating an irreducible complex space, gives a polyhedron homeomorphic to a normalization of the original space. It is also shown that this operation has the property of functoriality with respect to ramified coverings. A number of properties of such pseudomanifolds are obtained (in particular, it is shown that all of them are Cantor manifolds).
Bibliography: 9 titles.