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arXiv:1011.4640 [math.GT]AbstractReferencesReviewsResources

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

Vassily Olegovich Manturov

Published 2010-11-21, updated 2012-09-02Version 4

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.

Comments: One key argument is corrected; new projections satisfying the same properties are constructed
Categories: math.GT
Subjects: 57M25, 57M27
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