Generalized virtualization on welded links

Abstract

Let n be a positive integer. The aim of this paper is to study two local moves V (n) and V n on welded links, which are generalizations of the crossing virtualization. We show that the V (n)-move is an unknotting operation on welded knots for any n, and give a classification of welded links up to V (n)-moves. On the other hand, we give a necessary condition for which two welded links are equivalent up to V n -moves. This leads to show that the V n -move is not an unknotting operation on welded knots except for n = 1. We also discuss relations among V n -moves, associated core groups and the multiplexing of crossings.