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PARITY AND PROJECTION FROM VIRTUAL KNOTS TO CLASSICAL KNOTS

VASSILY OLEGOVICH MANTUROV

Peoples' Friendship University of Russia, Ordjonikidze St., 3, Moscow 117198, Russia

https://doi.org/10.1142/S0218216513500442Cited by:20 (Source: Crossref)

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. Such projections can be useful for lifting invariants from classical knots to virtual knots. Different maps satisfy different properties.

Keywords:

AMSC: 57M25, 57M27

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