Sebastian Baader
Published 2007-03-27Version 1
The Gordian distance between two knots measures how many crossing changes are needed to transform one knot into the other. It is known that there are always infinitely many non-equivalent knots `between' a pair of knots of Gordian distance two. In this paper we prove an extreme generalisation of this fact: there are knots with arbitrarily prescribed Vassiliev invariants between every pair of knots of Gordian distance two.
Comments: 7 pages, 8 figures
Blanchfield forms and Gordian distance
The Gordian distance of handlebody-knots and Alexander biquandle colorings
An obstruction of Gordian distance one and cosmetic crossings for genus one knots
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