Delta Moves and Arrow Polynomials of Virtual Knots
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\Delta -moves are closely related with a Vassiliev invariant of degree 2. For clas-sical knots, M. Okada showed that the second coe cients of the Conway polynomials oftwo knots di er by 1 if the two knots are related by a single \Delta -moves. The rst authorextended the Okada's result for virtual knots by using a Vassiliev invariant of virtual knotsof type 2 which is induced from the Kau man polynomial of a virtual knot. The arrowpolynomial is a generalization of the Kau man polynomial. We will generalize this resultby using Vassiliev invariants of type 2 induced from the arrow polynomial of a virtual knotand give a lower bound for the number of \Delta -movestransforming K1 to K2 if two virtualknots K1 and K2 are related by a nite sequence of \Delta-moves.
Abstract
\Delta -moves are closely related with a Vassiliev invariant of degree 2. For clas-sical knots, M. Okada showed that the second coe cients of the Conway polynomials oftwo knots di er by 1 if the two knots are related by a single \Delta -moves. The rst authorextended the Okada's result for virtual knots by using a Vassiliev invariant of virtual knotsof type 2 which is induced from the Kau man polynomial of a virtual knot. The arrowpolynomial is a generalization of the Kau man polynomial. We will generalize this resultby using Vassiliev invariants of type 2 induced from the arrow polynomial of a virtual knotand give a lower bound for the number of \Delta -movestransforming K1 to K2 if two virtualknots K1 and K2 are related by a nite sequence of \Delta-moves.
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