2022/11/01 by Danish Ali, Ali, Danish, Zhiqing Yang +3 · 1 citation
Computer Science · Mathematics · #57K10 #57K12 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2211.00459
openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An unknotting operation is a local move such that any knot diagram can be transformed into a diagram of the trivial knot by a finite sequence of these operations plus some Reidemeister moves. It is known that for all n ≥ 2 the H(n)-move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation H(n)-move to virtual knots and links. Virtualization and forbidden move are well-known unknotting operations for virtual knots and links. We also show that virtualization and forbidden move can be realized by a finite sequence of generalized Reidemeister moves and H(n)-moves.