Lesson plan
Bing double
(left) and its Bing double (right). In knot theory, a field of mathematics, the Bing double of a knot is a link with two components which follow the pattern of the knot and "hook together". Bing doubles were introduced in by their namesake, the American mathematician R. H. Bing. The Bing double of a slice knot is a slice link, though it is unknown whether the converse is true. The components of a Bing double bound disjoint Seifert surfaces. encasing the Bing double of the unknot. The Bing double of a knot is defined by placing the Bing double of the unknot in the solid torus surrounding it, as shown in the figure, and then twisting that solid torus into the shape of . This definition is similar to that for Whitehead doubles. The Bing double of the unknot is also called the Bing link.
Article summary
(left) and its Bing double (right). In knot theory, a field of mathematics, the Bing double of a knot is a link with two components which follow the pattern of the knot and "hook together". Bing doubles were introduced in by their namesake, the American mathematician R. H. Bing. The Bing double of a slice knot is a slice link, though it is unknown whether the converse is true. The components of a Bing double bound disjoint Seifert surfaces. encasing the Bing double of the unknot. The Bing double of a knot is defined by placing the Bing double of the unknot in the solid torus surrounding it, as shown in the figure, and then twisting that solid torus into the shape of . This definition is similar to that for Whitehead doubles. The Bing double of the unknot is also called the Bing link.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.