Oziride Manzoli Neto

Institute of Mathematical Science, University of São Paulo

E-mail: ozimneto@icmc.sc.usp.br

Let
be
a tubular neighborhood of an embedding of an
orientable manifold *F*^{k} in *S*^{k+2}.
In this work we define embeddings of
certain manifolds *M*^{k} in *V*_{F}.
These manifolds are defined in such a way that the map
restricted to *M* is an *n*-covering map of *F*^{k}.
We call these manifolds satellites of *F*^{k},
since it is a generalization of a satellite
construction in the classical case.
We study the relation between the Alexander Modules of
the two embeddings using a special decomposition
of the Abelian Covering
of
*S*^{k+2}-*V*_{M}.
For the case of orientable surfaces in *S*^{4} we are able to
get better relations and examples.