Notes for AKT-090917-2/0:27:14: Difference between revisions
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Rearranging the skein relation, we see that: |
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Using the skein relation, we see that <math>J(K_1)</math> has a factor of <math>x</math> where <math> K_1</math> is a knot with one double point. Analogously, for <math>K_{n+1}</math> - a knot with <math>k+1</math> double points, <math>J(K_{n+1})</math> will have a factor of <math>x^{n+1}</math>. In particular, the coefficient of <math>x^n</math>, <math>J_n</math>, will be zero. |
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:<math>J(\doublepoint)=x(...)</math> |
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Analogously, |
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:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math> |
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for n+1 double points. In particular, the coefficient of <math>x^n</math>, <math>J_n</math>, will be zero. |
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Revision as of 10:07, 8 September 2011
Rearranging the skein relation, we see that:
- Failed to parse (unknown function "\doublepoint"): {\displaystyle J(\doublepoint)=x(...)}
Analogously,
- Failed to parse (unknown function "\doublepoint"): {\displaystyle J(\doublepoint ... \doublepoint)=x^{n+1}(...)}
for n+1 double points. In particular, the coefficient of , , will be zero.
