Feature Column

Knots and Their Polynomials-5

 Knots and Their Polynomials


The calculation of the Jones polynomial of the right trefoil

We apply the skein relation to the right trefoil:

t-1J(right-trefoil)[t] -t J(right-trefoil-switched)[t] =(t1/2 - t-1/2)J(right-link)[t].

The second knot in the equation is topologically an unknot:

right-trefoil-switched =unknot,so J(right-trefoil-switched)[t] = 1,

and we are left with

J(right-trefoil)[t] =(t3/2 - t1/2)J(right-link)[t] + t2.

The knot on the right is made up of two linked unknots. This isa right-hand link because when we follow the orientation the two circles twist around each other to the right.

The next step is to analyze that link by the same method.


On to the next step.

Back to the previous knot page.

Back to the first knot page.

Welcome to the
Feature Column!

These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics.
Read more . . .

Search Feature Column

Feature Column at a glance


Show Archive

Browse subjects



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia