Year: 2026
Type: preprint
Abstract: Knotoid theory is a generalization of knot theory introduced by Turaev in 2012. In recent years, various invariants of knotoids have been studied. In this paper, we mainly discuss unknotting moves and unknotting numbers of plus-welded knotoids. Firstly, we prove that a descending diagram of a plus-welded knotoid can be transformed into a trivial one through a finite sequence of $Ω_1$, $VΩ_1 - VΩ_4$, $Ω_v$, $Φ_{\text{over}}$, and $Φ_+$-moves. Secondly, we extend the warping degree of knots to plus-welded knotoids and discuss its properties. Finally, by utilizing the descending diagram and the warping degree, we obtain two unknotting operations for plus-welded knotoids, referred as a crossing change and a crossing virtualization. For both operations, we find upper bounds for corresponding unknotting numbers of plus-welded knotoids.
Source: arXiv (Cornell University)
Authors: Li, Fengling, Vesnin, Andrei, Yang, Xuan
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2958620279, G5331045090
OpenAlex ID: W7125979448
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