Gordian distance and Vassiliev invariants

Sebastian Baader

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arXiv · math/0703786

Gordian distance and Vassiliev invariants

Sebastian Baader

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Abstract

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.

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Sebastian Baader. 2007-03-27. Gordian distance and Vassiliev invariants. https://arxiv.org/abs/math/0703786

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