Gordian distance and Vassiliev invariants

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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.
7 pages, 8 figures

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Geometric Topology, 57M25

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http://salesiana.dossiersoluciones.com/handle/123456789/126475

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703786
 http://arxiv.org/abs/math/0703786

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arXiv