Vassily Olegovich Manturov
Published 2011-07-25Version 1
The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical crossings. All previously known estimates for virtual crossing number were principally no more than linear in the number of classical crossings (or, what is the same, in the number of edges of a virtual knot diagram) and no virtual knot was found with virtual crossing number greater than the classical crossing number.
A lower bound on minimal number of colors for links
Minimal surface representations of virtual knots and links
Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves
![QR code for arXiv:1107.4828 [math.GT]](http://oss.arxitics.com/images/favicon.svg)