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arXiv · 1011.4640

A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity

Vassily Olegovich Manturov
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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.

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Vassily Olegovich Manturov. 2010-11-21. A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity. https://arxiv.org/abs/1011.4640

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