Full paper in PDF:
$%F. Hosokawa and S. Suzuki, On singular cut-and-pastes in the 3-space with applications to link theory, Rev. Mat. Univ. Complut. Madrid 8 (1995), no. 1, 155–168.%$

On Singular Cut-and-Pastes in the 3-Space with Applications to Link Theory

Fujitsugu HOSOKAWA and Shin’ichi SUZUKI

Department of Mathematics Kobe University Nada-ku, Kobe 657 — Japan	Department of Mathematics Waseda University Shinjuku-ku, Tokyo 169-50 — Japan

Received: February 25, 1994

ABSTRACT

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 $3 R$ which span the same trivial link are link-homotopic in the upper-half 4-space $3 R [0,8)$ keeping the link fixed.

Throughout the paper, we work in the piecewise linear category, consisting of simplicial complexes and piecewise linear maps.

1991 Mathematics Subject Classification: 57M25, 55P99.