Abstract
Let M be a compact connected orientable 3-manifold with non-empty boundary and f : M ! R a stable map. In this paper we study the existence of an immersion or embedding lift of f to R nV 3 with respect to the standard projection R ! R. We also characterize the orientable 3-dimensional handlebody in terms of stable maps which have only a restricted class of singularities. Moreover, by using the concept of an embedding lift of a certain map of a 2-dimensional polyhedron into R, we give a characterization of S.
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