Knots and Their Polynomials

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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

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

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].

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On to the next step.

Back to the previous step.

Back to the first knot page.