The aim of this paper is to study two local moves V (n) and V n on welded links for a positive integer n, 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 two welded links to be equivalent up to V n-moves. This leads us 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.
ASJC Scopus subject areas
- 数学 (全般)