Handlebody splittings of compact 3-manifolds with boundary.
The purpose of this paper is to relate several generalizations of the notion of the Heegaard splitting of a closed 3-manifold to compact, orientable 3-manifolds with nonempty boundary.
On singular cut-and-pastes in the 3-space with applications to link theory.
In the study of surfaces in 3-manifolds, the so-called ?cut-and-paste? of surfaces is frequently used. In this paper, we generalize this method, in a sense, to singular-surfaces, and as an application, we prove that two collections of singular-disks in the 3-space R3 which span the same trivial link are link-homotopic in the upper-half 4-space R3 [0,8) keeping the link fixed. Throughout the paper, we work in the piecewise linear category, consisting of simplicial complexes and piecewise linear maps....
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