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Unknotting moves of virtual knots
Unknotting moves, local deformations that can change any knot into the unknot, have long been a subject of interest in classical knot theory as they provide invariants that aid in distinguishing and cataloging knots. With the introduction of virtual knot theory, a generalization of classical knot theory that studies knots embedded not only in the sphere but in thickened spaces of higher genus as well, a new branch of study focusing on the unknotting moves of virtual knots was formed. It was quickly discovered that the sets of virtual unknotting moves and classical unknotting moves are primarily disjoint, meaning that few of the previously discovered classical moves generalized to virtual ones. Still, we can look to the classical moves to gain inspiration for new virtual unknotting moves. In this thesis, we present new virtual unknotting moves inspired by established classical and virtual unknotting moves.
DeVries, Melanie, "Unknotting moves of virtual knots" (2013). ETD collection for University of Nebraska - Lincoln. AAI3604714.