Knots and their polynomials

The Calculation of the Jones Polynomial of the Right Trefoil

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

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

This time the knot on the right is topologically an unknot

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

which gives

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

On to the next step.

Back to the previous step.

Back to the first knot page.