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.
57M25, 57M27
| Original language | English |
|---|---|
| Journal | Unknown Journal |
| Publication status | Published - 2018 Apr 26 |
| Externally published | Yes |
Keywords
- Alexander polynomial
- Arrow calculus
- Associated core group
- Elementary ideal
- Multiplexing of crossings
- Unknotting operation
- Virtualization
- Welded knot
- Welded link
ASJC Scopus subject areas
- General