A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity
Geometric Topology
2012-09-04 v4
Abstract
We construct various functorial maps (projections) from virtual knots to classical knots. These maps are defined on diagrams of virtual knots; in terms of Gauss diagram each of them can be represented as a deletion of some chords. The construction relies upon the notion of parity. As corollaries, we prove that the minimal classical crossing number for classical knots.
Cite
@article{arxiv.1011.4640,
title = {A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity},
author = {Vassily Olegovich Manturov},
journal= {arXiv preprint arXiv:1011.4640},
year = {2012}
}
Comments
One key argument is corrected; new projections satisfying the same properties are constructed