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AN UNKNOTTING OPERATION ON RIBBON 2-KNOTS
Preview AbstractWe define a local move on a ribbon 2-knot diagram, called an HC-move. We show that it is an unknotting operation for a ribbon 2-knot, and that the application of a single HC-move to a ribbon 2-knot changes the second derivative at t=1 of its normalized Alexander polynomial by either ±2 or 0. This result is applied to the calculation of the HC-unknotting numbers of ribbon 2-knots. We also consider a relation with a 1-handle unknotting operation.
VIRTUAL ARC PRESENTATIONS AND HC-MOVES OF RIBBON 2-KNOTS
Preview AbstractThe HC-move was defined as an unknotting operation of a ribbon 2-knot. Representing a ribbon 2-knot by a virtual arc, we see that the HC-move corresponds to one of the "forbidden moves", which unknot every virtual knot. Using this, we consider the α2-invariant of a ribbon 2-knot and a relation between the Δ-move for a 1-knot and the HC-move for its spun 2-knot.