Polynomial Unknotting and Singularity Index
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초록
We introduce a new method to transform a knot diagram into a diagram of an unknot using a polynomial representation of the knot. Here the unknotting sequence of aknot diagram with least number of crossing changes can be realized by a family of polynomial maps. The number of singular knots in this family is defined to be the{\it singularity index} of the diagram. We show that the singularity index of a diagram is always less than or equal to its unknotting number.
Abstract
We introduce a new method to transform a knot diagram into a diagram of an unknot using a polynomial representation of the knot. Here the unknotting sequence of aknot diagram with least number of crossing changes can be realized by a family of polynomial maps. The number of singular knots in this family is defined to be the{\it singularity index} of the diagram. We show that the singularity index of a diagram is always less than or equal to its unknotting number.
참고문헌 (16)
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