This MedLibrary.org supplementary page on Writhe is provided directly from the open source Wikipedia as a service to our readers. Please see the note below on authorship of this content, as well as the Wikipedia usage guidelines. To search for other content from our encyclopedia supplement, please use the form below:
Related Sponsors
In knot theory, the writhe is a property of an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings.
A direction is assigned to the link at a point in each component and this direction is followed all the way around each component. If as you travel along a link component and cross over a crossing, the strand underneath goes from right to left, the crossing is positive; if the lower strand goes from left to right, the crossing is negative. One way of remembering this is to use a variation of the right-hand rule.
 |
 |
|
| Positive crossing |
Negative crossing |
For a knot diagram, using the right-hand rule with either orientation gives the same result, so the writhe is well-defined on unoriented knot diagrams.
The writhe of a knot is unaffected by two of the three Reidemeister moves: moves of Type II and Type III do not affect the writhe. Reidemeister move Type I, however, increases or decreases the writhe by 1. This implies that the writhe of a knot is not an isotopy invariant of the knot itself — only the diagram. By a series of Type I moves one can set the writhe of a diagram for a given knot to be any integer at all.
See also
Wikipedia content modification information:
- This page was last modified on 4 March 2008, at 16:59.
Wikipedia Authorship and Review
Wikipedia content provided here is not reviewed directly by MedLibrary.org. Wikipedia content is authored by an open community of volunteers and is not produced by or in any way affiliated with MedLibrary.org.
Wikipedia Usage Guidelines
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article on "Writhe".
The URL for this specific entry is:
All Wikipedia text is available under the terms of the GNU Free Documentation License. (See Copyrights for details). Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc.