The warping polynomial of a knot diagram

Details The warping polynomial of a knot diagram The warping polynomial of a knot diagram

2011-09-27

arxiv.org/abs/1109.5898v2

Mathematics

Geometric Topology

21 pages, 18 figures

Scientific paper

We introduce the warping polynomial of an oriented knot diagram. In this paper, we characterize the warping polynomial, and define the span of a knot to be the minimal span of the warping polynomial for all diagrams of the knot. We show that the span of a knot is one if and only if it is non-trivial and alternating, and we give an inequality between the span and the dealternating number.

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