Quantization of the crossing number of a knot diagram
Geometric Topology
2011-12-20 v2
Abstract
We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for all the states for the plane curve. As an application, we show that every closed transversely intersected plane curve with even crossing points has two independent canonical orientations and every based closed transversely intersected plane curve with odd crossing points has two independent canonical orientations.
Keywords
Cite
@article{arxiv.1112.1809,
title = {Quantization of the crossing number of a knot diagram},
author = {Akio Kawauchi and Ayaka Shimizu},
journal= {arXiv preprint arXiv:1112.1809},
year = {2011}
}
Comments
14 pages, 14 figures