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

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

2010-11-21

arxiv.org/abs/1011.4640v3

Mathematics

Geometric Topology

A gap was found in the proof of the main theorem

Scientific paper

We construct a functorial map (projection) from virtual knots to classical knots. This map is defined on diagrams of virtual knots. The construction relies on the notion of parity. As corollaries, we prove that the minimal classical crossing number for classical knots is realised by classical diagrams only and that the shortest chain of Reidemeister moves connecting two classical diagrams consists of classical diagrams only.

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