Gordian distance and Vassiliev invariants

Details Gordian distance and Vassiliev invariants Gordian distance and Vassiliev invariants

2007-03-27

arxiv.org/abs/math/0703786v1

Mathematics

Geometric Topology

7 pages, 8 figures

Scientific paper

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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