Notes for AKT-090917-2/0:27:14 - Revision history

Iva at 15:14, 8 September 2011

2011-09-08T15:14:32Z

← Older revision		Revision as of 11:14, 8 September 2011
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	Analogously,		Analogously,
	:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math>		:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math>
	for n+1 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>k+1</math> double points.		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.

Iva at 15:13, 8 September 2011

2011-09-08T15:13:21Z

← Older revision		Revision as of 11:13, 8 September 2011
Line 3:		Line 3:
	Analogously,		Analogously,
	:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math>		:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math>
	for n+1 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>k+1</math> ~~crossings~~.		for n+1 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>k+1</math> double points.

Iva at 15:12, 8 September 2011

2011-09-08T15:12:35Z

← Older revision		Revision as of 11:12, 8 September 2011
Line 3:		Line 3:
	Analogously,		Analogously,
	:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math>		:<math>J(\doublepoint ... \doublepoint)=x^{n+1}(...)</math>
	for n+1 double points. In particular, the coefficient of <math>x^n</math>, <math>J_n</math>, will be zero.		for n+1 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>k+1</math> crossings.

Iva at 15:07, 8 September 2011

2011-09-08T15:07:21Z

← Older revision		Revision as of 11:07, 8 September 2011
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			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 n+1 double points. In particular, the coefficient of <math>x^n</math>, <math>J_n</math>, will be zero.

Iva at 15:03, 8 September 2011

2011-09-08T15:03:22Z

New page

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.