Whitehead link

In knot theory, the Whitehead link, discovered by J.H.C. Whitehead, is one of the most basic links.

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.

Related Topics:
Unknot - Reidemeister Type I move - Linking number

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In braid theory notation, the link is written

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:sigma^2_1sigma^2_2sigma^{-1}_1sigma^{-2}_2.,

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Its Jones polynomial is

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:V(t)=t^{- {3 over 2}}(-1+t-2t^2+t^3-2t^4+t^5).

~ ~ ~ ~ ~ ~ ~ ~ ~ ~