Virtualized Delta moves for virtual knots and links

Abstract

We introduce a local deformation called the virtualized $Δ$-move for virtual knots and links. We prove that the virtualized $Δ$-move is an unknotting operation for virtual knots. Furthermore we give a necessary and sufficient condition for two virtual links to be related by a finite sequence of virtualized $Δ$-moves.

Figures (17)

• Figure 1.1: A virtualized $\Delta$-move
• Figure 2.1: Proof of Lemma \ref{['lem-cc']}
• Figure 2.2: A local deformation FD
• Figure 2.3: Proof of Lemma \ref{['lem-fd']}
• Figure 2.4: An upper forbidden move

Theorems & Definitions (41)

• Definition 1.1
• Definition 1.2
• Theorem 1.3
• Theorem 1.4
• Theorem 1.5
• Lemma 2.1
• proof
• Lemma 2.2
• proof
• Remark 2.3