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.
@article{urn:eudml:doc:44183,
title = {On singular cut-and-pastes in the 3-space with applications to link theory.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {8},
year = {1995},
pages = {155-168},
zbl = {0835.57005},
mrnumber = {MR1356440},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44183}
}
Hosokawa, Fujitsugu; Suzuki, Shin'ichi. On singular cut-and-pastes in the 3-space with applications to link theory.. Revista Matemática de la Universidad Complutense de Madrid, Tome 8 (1995) pp. 155-168. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44183/