The support of global graph links
Koichi Yano · Journal of the Mathematical Society of Japan · 1985
establish the following (see sections 1 and 3 for terminology). CHARACTERIZATION OF GLOBAL GRAPH LINKS. Every graph link is obtainedfrom elementary ones by a finite number of operatjOns of disjoint union, adding a cable, replacjng by a cable, link connected sum and self link connected sum.This was known for graph knots in $S^{3}$ by Gordon [4] and Ue [18] (see also Soma [13] and Eisenbud-Neumann [3]).In section 4 we study how the support changes by the operations in this theorem and the main results are proved in section 5. Finally in section 6, we study Dehn surgeries along graph knots as an application of $\mathcal{R}$ -decompositions and prove THEOREM.All but two Dehn surgeries along a graph knot with irreducible exterior yield irreducible manifolds.A part of this paper was announced in [20].