Notes for AKT-090917-2/0:27:14: Difference between revisions

Latest revision as of 11:14, 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 $x^{n}$ , $J_{n}$ , will be zero when evaluated on a knot with $n+1$ double points.

@@ Line 1: / Line 1: @@
+Rearranging the skein relation, we see that:
-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.
+:<math>J(\doublepoint)=x(...)</math>
+Analogously,
+:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math>
+for <math>n+1</math> double points. In particular, the coefficient of <math>x^n</math>, <math>J_n</math>, will be zero when evaluated on a knot with <math>n+1</math> double points.