Notes for AKT-090910-1/0:45:11: Difference between revisions
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These suffice because for any knot or link diagram we can apply the first relation recursively until we eliminate all the crossings and end up with a disjoint union of unknots. |
These suffice because for any knot or link diagram we can apply the first relation recursively until we eliminate all the crossings and end up with a disjoint union of unknots. |
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For instance, we get: |
For instance, we get: |
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<math>\left\langle \HopfLink \right\rangle = A^2d^2 + 2ABd + B^2d^2</math> |
<math>\left\langle \HopfLink \right\rangle = A^2d^2 + 2ABd + B^2d^2</math> |
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Latest revision as of 22:21, 27 August 2011
The Kauffman bracket is completely determined by the relations:
- [math]\displaystyle{ \left\langle\slashoverback\right\rangle=A\left\langle\hsmoothing\right\rangle + B \left\langle\smoothing\right\rangle }[/math]
- [math]\displaystyle{ \left\langle \bigcirc^k \right\rangle = d^k }[/math]
These suffice because for any knot or link diagram we can apply the first relation recursively until we eliminate all the crossings and end up with a disjoint union of unknots. For instance, we get:
[math]\displaystyle{ \left\langle \HopfLink \right\rangle = A^2d^2 + 2ABd + B^2d^2 }[/math]
