Abstract
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.
Original language | English |
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Pages (from-to) | 923-944 |
Number of pages | 22 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 72 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Alexander polynomial
- Arrow calculus
- Associated core group
- Multiplexing of crossings
- Unknotting operation
- Virtualization
- Welded knot
- Welded link
ASJC Scopus subject areas
- Mathematics(all)