Hopf Link

Author

Eric W. Weisstein
July 25, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/KnotTheory/HopfLink.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HopfLink.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Knots`Knots`;

Symbol

TraditionalForm[link=HopfLink]

Braid Word

BraidWord[link]//TraditionalForm

Properties

Through[{Arf,LinkCrossingNumber,AmphichiralQ,InvertibleQ}[link]]

Polynomials

AlexanderNabla[link,{x,y}]

BLMHoQ[link,x]//TraditionalForm

HomflyP[link,{ℓ,m}]//TraditionalForm

JonesV[link,t]//TraditionalForm

KauffmanF[link,{a,z}]//TraditionalForm

Figure

Show[ClosedBraid[BraidWord[link],Style->Tube]]