Knot at Lunch, May 24, 2007 - Revision history

Drorbn at 17:46, 24 May 2007

2007-05-24T17:46:25Z

← Older revision		Revision as of 13:46, 24 May 2007
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	* <math>[abw]=[baw]</math> if <math>\|w\|\geq 2</math> and similar identities.		* <math>[abw]=[baw]</math> if <math>\|w\|\geq 2</math> and similar identities.
	* <math>\phi(a,b,c)=\phi(a,b)</math>, <math>\Phi=\exp\phi</math> and in our case, this is just <math>1+\phi</math>!		* <math>\phi(a,b,c)=\phi(a,b)</math>, <math>\Phi=\exp\phi</math> and in our case, this is just <math>1+\phi</math>!
			* <math>[a^nb^mab]=(-1)^{n+m}[ab]a^nb^m</math>.
			* <math>\phi=[ab]\lambda(a,b)</math>. With this, we have as follows:
			* Unitarity becomes <math>\lambda(a,b)=\lambda(b,a)</math>.
			* <math>\Phi^{312}=1+[ca]\lambda(ac)</math> where <math>c=-a-b</math>.
			* Likewise for all other terms in the hexagon, which becomes
			{{Equation*\|<math>e^{b+c}=(1+[ab]\lambda(a,b))e^b\cdots = e^be^c+[ab]\left(\lambda(a,b)e^{b+c}+\lambda(b,c)e^c+\lambda(a,c)\right)</math>}}
			* Simplifying <math>e^{b+c}-e^be^c</math> using frozen feet, this becomes
			{{Equation*\|<math>[cb]\left(\frac{e^{b+c}-1-b-c}{b(b+c)}-\frac{e^c-1-c}{c}\right) = [ab]\left(\lambda(a,b)e^{b+c}+\lambda(b,c)e^c+\lambda(a,c)\right)</math>}}
			* Alternatively,
			{{Equation*\|<math>[ab]\left(\ldots\right) = [ab]\left(\lambda(a,b)e^{b+c}+\lambda(b,c)e^c+\lambda(a,c)\right)</math>}}

Drorbn at 17:04, 24 May 2007

2007-05-24T17:04:12Z

← Older revision		Revision as of 13:04, 24 May 2007
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	* The action of <math>\Delta</math>, <math>\eta_i</math>, and of <math>\star\mapsto\star^{23}</math>, etc. ({{Dror}}: see also [[VS, TS and TG Algebras]].)		* The action of <math>\Delta</math>, <math>\eta_i</math>, and of <math>\star\mapsto\star^{23}</math>, etc. ({{Dror}}: see also [[VS, TS and TG Algebras]].)
	* Generators and relations: <math>R^\pm</math>, <math>\Phi^\pm</math>, the hexagons and pentagon, unitarity, non-degeneracy, group-like property.		* Generators and relations: <math>R^\pm</math>, <math>\Phi^\pm</math>, the hexagons and pentagon, unitarity, non-degeneracy, group-like property.
	* <math>[abw]=[baw]</math> if <math>\|w\|\geq 2</math>.		* <math>[abw]=[baw]</math> if <math>\|w\|\geq 2</math> and similar identities.
			* <math>\phi(a,b,c)=\phi(a,b)</math>, <math>\Phi=\exp\phi</math> and in our case, this is just <math>1+\phi</math>!

Drorbn at 16:55, 24 May 2007

2007-05-24T16:55:23Z

← Older revision		Revision as of 12:55, 24 May 2007
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	* Definition of <math>{\mathcal A}^n</math> and its relation with finite type invariants.		* Definition of <math>{\mathcal A}^n</math> and its relation with finite type invariants.
	* The frozen feet quotient.		* The frozen feet quotient.
	* The action of <math>\Delta</math> and of <math>\star\mapsto\star^{23}</math>, etc. ({{Dror}}: ~~See~~ also [[VS, TS and TG Algebras]].)		* The action of <math>\Delta</math>, <math>\eta_i</math>, and of <math>\star\mapsto\star^{23}</math>, etc. ({{Dror}}: see also [[VS, TS and TG Algebras]].)
	* Generators and relations: <math>R^\pm</math>, <math>\Phi^\pm</math>, the hexagons and pentagon.		* Generators and relations: <math>R^\pm</math>, <math>\Phi^\pm</math>, the hexagons and pentagon, unitarity, non-degeneracy, group-like property.
			* <math>[abw]=[baw]</math> if <math>\|w\|\geq 2</math>.

Drorbn at 16:41, 24 May 2007

2007-05-24T16:41:34Z

← Older revision		Revision as of 12:41, 24 May 2007
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	First meeting for summer 2007! Peter Lee is telling us about associators with frozen feet. See also his handout from the [[CMS Winter 2006 Session on Knot Homologies]] - front: [[Image:CMS 2006 Lee Handout Front.png\|80px]], back: [[Image:CMS 2006 Lee Handout Back.png\|80px]] and {{Dror}}'s very partial [[paperlet]], [[Associators with Frozen Feet]].		First meeting for summer 2007! Peter Lee is telling us about associators with frozen feet. See also his handout from the [[CMS Winter 2006 Session on Knot Homologies]] - front: [[Image:CMS 2006 Lee Handout Front.png\|80px]], back: [[Image:CMS 2006 Lee Handout Back.png\|80px]] and {{Dror}}'s very partial [[paperlet]], [[Associators with Frozen Feet]].

			* Definition of <math>{\mathcal A}^n</math> and its relation with finite type invariants.
			* The frozen feet quotient.
			* The action of <math>\Delta</math> and of <math>\star\mapsto\star^{23}</math>, etc. ({{Dror}}: See also [[VS, TS and TG Algebras]].)
			* Generators and relations: <math>R^\pm</math>, <math>\Phi^\pm</math>, the hexagons and pentagon.

Drorbn at 16:25, 24 May 2007

2007-05-24T16:25:09Z

← Older revision		Revision as of 12:25, 24 May 2007
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			{{KAL/Navigation}}

	First meeting for summer 2007! Peter Lee is telling us about associators with frozen feet. See also his handout from the [[CMS Winter 2006 Session on Knot Homologies]] - front: [[Image:CMS 2006 Lee Handout Front.png\|80px]], back: [[Image:CMS 2006 Lee Handout Back.png\|80px]] and {{Dror}}'s very partial [[paperlet]], [[Associators with Frozen Feet]].		First meeting for summer 2007! Peter Lee is telling us about associators with frozen feet. See also his handout from the [[CMS Winter 2006 Session on Knot Homologies]] - front: [[Image:CMS 2006 Lee Handout Front.png\|80px]], back: [[Image:CMS 2006 Lee Handout Back.png\|80px]] and {{Dror}}'s very partial [[paperlet]], [[Associators with Frozen Feet]].

Drorbn at 16:24, 24 May 2007

2007-05-24T16:24:20Z

New page

First meeting for summer 2007! Peter Lee is telling us about associators with frozen feet. See also his handout from the [[CMS Winter 2006 Session on Knot Homologies]] - front: [[Image:CMS 2006 Lee Handout Front.png|80px]], back: [[Image:CMS 2006 Lee Handout Back.png|80px]] and {{Dror}}'s very partial [[paperlet]], [[Associators with Frozen Feet]].