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 unlinked unknots

• Step 3: the Jones Polynomial of two unlinked unknots

• Step 4: Working backwards to the answer

[t] = (t^3/2 - t^1/2) [t] + t² (Step 1)

= (t^3/2 - t^1/2)(t^3/2 - t^1/2 + t² [t]) + t² (Step 2)

= (t^3/2 - t^1/2)(t^3/2 - t^1/2 + t²(- t^1/2 - t^-1/2)) + t² (Step 3)

= -t⁴ + t³ + t.

This completes the calculation.

Back to the previous step.

Back to the first knot page.