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Encyclopedia > Whitehead link
The Whitehead link
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The Whitehead link

In knot theory, the Whitehead link, discovered by J.H.C. Whitehead, is one of the most basic links. Trefoil knot, the simplest non-trivial knot. ... John Henry Constantine Whitehead (11 November 1904- 8 May 1960), known as Henry, was a British mathematician who was one of the founders of homotopy theory. ... The Borromean rings, a link with three components each equivalent to the unknot. ...


J.H.C. Whitehead spent much of the 1930s looking for a proof of the Poincaré conjecture. In 1934 the Whitehead link was used as part of his construction of the now-named Whitehead manifold, which refuted his previous purported proof of the conjecture. In mathematics, the Poincaré conjecture (IPA: [])[1] is a conjecture about the characterization of the three-dimensional sphere amongst three-dimensional manifolds. ... 1934 (MCMXXXIV) was a common year starting on Monday (link will take you to calendar). ... In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to . ...

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Structure

The link is created with two projections of the unknot: one circular loop and one figure eight-shaped (i.e., a loop with a Reidemeister Type I move applied) loop intertwined such that they are inseparable and neither loses its form. Excluding the instance where the figure eight thread intersects itself, the Whitehead link has four crossings. Because each underhand crossing has a paired upperhand crossing, its linking number is 0. The unknot, and a knot equivalent to it The unknot is a loop of rope without a knot in it (in knot theory, ropes have no ends; they are loops). ... Trefoil knot, the simplest non-trivial knot. ... In mathematics, the linking number is a simple invariant for links (i. ...


In braid theory notation, the link is written In topology, braid theory is an abstract geometric theory studying the everyday braid concept, and some generalisations. ...

Its Jones polynomial is This article needs cleanup. ...

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References

Weisstein, Eric W., Whitehead link at MathWorld. MathWorld is an online mathematics reference work, sponsored by Wolfram Research Inc. ...


  Results from FactBites:
 
J. H. C. Whitehead - Wikipedia, the free encyclopedia (244 words)
John Henry Constantine Whitehead (11 November 1904- 8 May 1960), known as Henry, was a British mathematician who was one of the founders of homotopy theory.
The Whitehead problem on abelian groups was solved (as an independence proof) by Saharon Shelah.
He was the nephew of Alfred North Whitehead.
93-STENGERS-WHITEHEAD (5680 words)
This does not mean that IS is going to champion Whitehead’s attempts to account for Einstein’s relativity, quantum physics, and Darwinian evolutionary theory by gathering new and better proofs borrowed from her own experience of contemporary science —for instance by drawing on her long association with Ilya Prigogine.
If Whitehead is difficult—if IS is sometimes difficult, too—it is because they both have to climb back up a steeper slope than the one Sisyphus had to ascend, and with a heavier load than he had, too.
Whitehead always digs further in what is given by the scientific activity and what is learned about the world in addition to what scientists say about their own work.
  More results at FactBites »


 

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