TOPICS
Search

Whitehead Link

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
WhiteheadLink

The prime link 05-0201, illustrated above, with braid word sigma_1^2sigma_2^2sigma_1^(-1)sigma_2^(-2) or sigma_1sigma_2^(-1)sigma_1sigma_2^(-2) and Jones polynomial

V(t)=t^(-3/2)(-1+t-2t^2+t^3-2t^4+t^5).

The Whitehead link has linking number 0. It was discovered by Whitehead in 1934 (Whitehead 1962, pp. 21-50) as a counterexample to a piece of an attempted proof of the Poincaré conjecture (Milnor).

See also

Borromean Rings, Hopf Link, Link, Poincaré Conjecture, Prime Link, Unlink

Explore with Wolfram|Alpha

References

Kauffman, L. Knots and Physics. Teaneck, NJ: World Scientific, p. 36, 1991.Livingston, C. Knot Theory. Washington, DC: Math. Assoc. Amer., pp. 9 and 37-38, 1993.Milnor, J. "The Poincaré Conjecture." http://www.claymath.org/millennium/Poincare_Conjecture/Official_Problem_Description.pdf.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 68, 72, and 137, 1976.Whitehead, J. H. C. Mathematical Works, Vol. 2. London: Pergamon Press, pp. 21-50, 1962.

Referenced on Wolfram|Alpha

Whitehead Link

Cite this as:

Weisstein, Eric W. "Whitehead Link." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WhiteheadLink.html

Subject classifications