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http://dx.doi.org/10.5666/KMJ.2014.54.2.271

Polynomial Unknotting and Singularity Index  

Mishra, Rama (Indian Institute of Science Education and Research)
Publication Information
Kyungpook Mathematical Journal / v.54, no.2, 2014 , pp. 271-292 More about this Journal
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 a knot 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 singularity index of the diagram. We show that the singularity index of a diagram is always less than or equal to its unknotting number.
Keywords
unknotting number; double point; immersion;
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