Distortion
Twisting of (also: swirl , Eng .: writhe ) referred to in the knot theory , a branch of topology in mathematics, a property-oriented Verschlingungsdiagramme , among other things, in the definition of the Jones polynomial is used. The twist is the difference between the number of positive crossings and the number of negative crossings .
Positive and negative crossings are defined according to the pictures below.
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| Positive crossover |
Negative crossover |
For node diagrams , the twist is independent of the selected orientation, for interlacing diagrams with more than one component it is generally not.
The twist is invariant under Reidemeister movements of type II and III. Type I Reidemeister movements increase or decrease the twisting by 1. In particular, the twisting is not a knot invariant , but only an invariant of the knot diagram.
literature
- Colin C. Adams: The Knot Book. An elementary introduction to the mathematical theory of knots. 1994; 2004, ISBN 0-8218-3678-1
- The knot book. Introduction to the mathematical theory of knots. Spectrum, Heidelberg / Berlin / Oxford 1995, ISBN 3-86025-338-7