Knot at Lunch on October 23 2008

Knot at Lunch/Navigation  Date(s) Link(s) 2010/02/22 ??? 2010/01/20 Formal integration 2010/01/13 Combing wB 2010/01/06 Exponentiation in tder 2009/09/22 descending v-knots 2009/08/26 red over green v-tangles 2009/08/19 Polyak Algebra 2009/07/08 Immanants 2009/07/01 Alexander modules 2009/06/24 Alexander modules 2009/06/10 Alexander, PBW for A^w, class videos 2009/06/03 Low key 2009/05/06 Low key 2009/04/29 Winter on Ribbons 2009/04/22 Misc 2009/04/15 KV 2009/03/25 KV 2009/03/18 Peter Lee 2009/03/04 Kirby calculus 2009/02/25 Karene on Reidemeister-Schreier 2009/02/11 Dror on Trotter, Jana on Alexander 2009/02/04 Bracelets 2009/01/28 gl(N) chickens 2009/01/15 2D Gauss Diagrams, FiC 2009/01/08 S&G update and more 2008/12/11 Chu on Garside, II 2008/12/04 wZ is 1-1 2008/11/27 The Wen 2008/11/20 The Zoom Space 2008/11/13 Chu on Garside 2008/11/06 Z and GPV 2008/10/30 Peter Lee on EHKR 2008/10/23 Map of the Field 2008/09/25 Hirasawa on Open Books 2008/09/18 Odd Khovanov 2008/09/17 Categorification.m 2008/09/11 More wAlex 2008/09/03 ? 2008/08/27 Dexp and BCH 2008/08/06 Z, A, det, tr, log 2008/07/30 Alexander Relations Marathon 2008/07/02 Peter Lee on horizontal Aw 2008/06/25 w-Alexander 2008/06 16-22 Thomas Fiedler Marathon 2008/06/11 ? 2008/06/04 Dylan Thurston 2008/05/28 Welded Tangles 2008/05/21 Bruce, Lucy 2008/04/23 Welded Knots 2008/04/16 Quandles and Lie algebras 2008/04/09 No-div Alekseev-Torossian 2008/04/02 Knotted Kung Fu Pandas 2008/03/26 Homotopy invariants 2008/03/19 Infinitesimal Artin 2008/03/12 Infinitesimalization of Artin 2008/03/05 Krzysztof Putyra on Odd Khovanov Homology 2008/02/27 Karene Chu on Proof of Artin 2008/02/20 Organizational, Hecke algebras 2008/02/13 Exponential and Magnus expansions 2008/02/06 cancelled 2008/01/30 Artin's theorem 2008/01/16 Hutchings' work, 2 2008/01/09 Hutchings' work, 1 2007/12/12 Bone soup 2007/12/05 Expansions 2007/11/28 Quantum groups 2007/11/21 Surfaces and gl(N)/so(N) 2007/11/07 Expansions for Groups 2007/10/31 Louis Leung on bialgebra weight systems 2007/10/24 Zsuzsi Dancso, continued 2007/10/17 Jana Archibald on the multivariable Alexander 2007/10/10 Zsuzsi Dancso on diagrammatic su(2) 2007/10/03 Hernando Burgos on alternating tangles 2007/09/26 Peter Lee on homology 2007/09/06 Garoufalidis' visit 2007/08/30 Art and enumeration 2007/08/23 My Hanoi talk? 2007/08/16 Lie bialgebra weight systems and more 2007/07/19 Subdiagram formulas 2007/07/12 Playing with Brunnians 2007/07/05 Virtualization 2007/06/28 Virtual braids 2007/06/07 Virtual knots 2007/05/31 Social gathering 2007/05/24 Lee on Frozen Feet

Invitation

Dear Knot at Lunch People,

We will have our next lunch on Thursday October 23, at the (new and hopefully temporary) usual place, the seminar room on the 10th floor of 215 Huron St., at 12 noon.

As always, please bring brown-bag lunch and fresh ideas. I'm hoping to make a little map-handout, roughly showing the logical relations between all those things I am confused about. If the map will be ready by Thursday, we may talk about it. If not, we'll have to find something else to talk about.

Further information about this Knot at Lunch meeting may be posted later at https://drorbn.net/drorbn?title=Knot_at_Lunch_on_October_23_2008.

As always, if you know anyone I should add to this mailing list or if you wish to be removed from this mailing list please let me know. To prevent junk accumulation in mailboxes, I will actively remove inactive people unless they request otherwise.

Best,

Dror.

Blackboard Shots

See BBS/KAL-081023-135536.jpg.

The Gospel in $v$, $w$ and Seven $Z$'s

	$Z:B\to {\mathcal {A}}^{h}$	Classifies braids! Detected by Lie algebras!
1	$Z:{\mathcal {K}}(\bigcirc )\to {\mathcal {A}}(\bigcirc )$	Related to metrized Lie algebras! This is the Kontsevich integral!	Related to Chern-Simons theory and configuration space integrals! Has GPV formulas!
2	$Z:{\mathcal {K}}^{TG}\to {\mathcal {A}}^{TG}$	Enables "Algebraic Knot Theory"! Finitely presented! Related to Drinfel'd associators!	No-go theorems in bounded degrees. Extremely challenging to compute. Leads to "internal quotients"! Still challenging to compute.
	$Z:pT\to {\mathcal {A}}^{pT}$	Does not exist.
	The modifier v means "virtual". Chords become arrows, planar algebras become circuit algebras and $4T$ becomes $6T$. "Algebraic Knot Theory" concepts still apply!
	The modifier w means "welded" or "weakly virtual". Overcrossings commute, tails commute.
3	$Z:wB\to {\mathcal {A}}^{wh}$	Ribbon tori in ${\mathbb {R} }^{4}$! Flying rings in ${\mathbb {R} }^{3}$! Easy formulas for $Z$!	Relates to $\operatorname {Aut} (F_{n})$! Classifies w-braids!
4	$Z:w{\mathcal {K}}(\bigcirc )\to {\mathcal {A}}^{w}(\bigcirc )$	Related to the Alexander polynomial! Related to general Lie algebras! Related to co-commutative Lie bi-algebras!	Related to BF theory!
5	$Z:w{\mathcal {T}}\to {\mathcal {A}}^{wT}$	Still easy! Related (by other means) to free Lie algebras, derivations, traces!
6	$Z:w{{\mathcal {T}}T}\to {\mathcal {A}}^{wTT}$	Related to the Kashiwara-Vergne conjecture and the orbit method! Via Alekseev-Torrosian, explicit tree-level formulas for associators!
7	$Z:v{{\mathcal {T}}T}\to {\mathcal {A}}^{vTT}$	Related to general Lie bialgebras, Etingof-Kazhdan and quantum groups in general!