Knots and their polynomials

The Calculation of the Jones Polynomial of the Right Trefoil

• Step 1: from the Right Trefoil to the Right Link

• Step 2: from the Right Link to two linked unknots

• Step 3: the Jones Polynomial of two unlinked unknots

• Step 4: working backwards to the answer

t^-1[t] - t [t] = (t^1/2 - t^-1/2) [t].

This time the knot on the right is topologically an unknot

= , so [t] = 1,

which gives

[t] = t^3/2 - t^1/2 + t² [t].

Back to the previous step.

Back to the first knot page.