Diagrams realizing prescribed sublink diagrams for virtual links and welded links

Abstract

Jin and Lee [3] proved the following: Suppose that D1, . . . , Dn are link diagrams. Given a link L which is partitioned into sublinks L1, . . . , Ln admitting diagrams D1, . . . , Dn respectively, there is a diagram D of L whose restrictions to L1, . . . , Ln are isotopic to D1, . . . , Dn, respectively. In this paper we show that a similar result does hold for welded links and does not for virtual links.