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wClips-120125-1

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Videography by Zsuzsanna Dancso troubleshooting

Notes on wClips-120125-1:    [edit, refresh]

Section 2.2.3 - basis conjugating automorphisms of F_n.


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Announcements. small circle, UofT, LDT Blog (also here). Email Dror to join our mailing list!

Resources. How to use this site, Dror's notebook, blackboard shots.

The wClips

http://katlas.math.toronto.edu/drorbn/dbnvp/dbnvp.png
Date Links
Jan 11, 2012 dbnvp 120111-1: Introduction.
dbnvp 120111-2: Section 2.1 - v-Braids.
Jan 18, 2012 dbnvp 120118-1: An introduction to this web site.
dbnvp 120118-2: Section 2.2 - w-Braids by generators and relations and as flying rings.
dbnvp 120118-3: Section 2.2 - w-Braids - other drawing conventions, "wens".
Jan 25, 2012 dbnvp 120125-1: Section 2.2.3 - basis conjugating automorphisms of F_n.
dbnvp 120125-2: A very quick introduction to finite type invariants in the "u" case.
Feb 1, 2012 dbnvp 120201: Section 2.3 - finite type invariants of v- and w-braids, arrow diagrams, 6T, TC and 4T relations, expansions / universal finite type invariants.
Feb 8, 2012 dbnvp 120208: Review of u,v, and w braids and of Section 2.3.
Feb 15, 2012 dbnvp 120215: Section 2.5 - mostly compatibilities of Z^w, also injectivity and uniqueness of Z^w.
Feb 22, 2012 dbnvp 120222: Section 2.5.5, \alpha:{\mathcal A}^u\to{\mathcal A}^v, and Section 3.1 (partially), the definition of v- and w-knots.
Feb 29, 2012 dbnvp 120229: Sections 3.1-3.4: v-Knots and w-Knots: Definitions, framings, finite type invariants, dimensions, and the expansion in the w case.
Mar 7, 2012 dbnvp 120307: Section 3.5: Jacobi diagrams and the bracket-rise theorem.
Mar 14, 2012 dbnvp 120314: Section 3.6 - the relation with Lie algebras.
Mar 21, 2012 dbnvp 120321: Section 4 - Algebraic Structures.
Mar 28, 2012 Out-of-sequence not-on-tape we watched the video of Talks: GWU-1203.
Apr 4, 2012 dbnvp 120404: Section 3.7 - The Alexander Theorem (statement).
Apr 18, 2012 dbnvp 120418: Aside on the Euler trick, the differential of \exp, and the BCH formula.
Apr 25, 2012 dbnvp 120425: Section 3.8, a disorganized lecture towards the proof of the Alexander theorem.
May 2, 2012 dbnvp 120502: Section 4: Algebraic structures (review), circuit algebras, v- and w-tangles.
May 10, 2012 dbnvp 120510: Sections 5.1 and 5.2: tangles, their projectivization and its relationship with Alekseev-Torossian spaces.
May 23, 2012 dbnvp 120523: Section 5.2: Proof of the relationship with A-T spaces.
May 30, 2012 dbnvp 120530: Interpreting {\mathcal A}^w(\uparrow_n) as a universal space of invariant tangential differential operators.
wClips Seminar Group Photo
Group photo on January 11, 2012: DBN, ZD, Stephen Morgan, Lucy Zhang, Iva Halacheva, David Li-Bland, Sam Selmani, Oleg Chterental, Peter Lee.
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0:00:00 [edit] We started with two handouts:

http://katlas.math.toronto.edu/drorbn/AcademicPensieve/Classes/12-wClips/thumbs/HowToUseThisSite.png http://katlas.math.toronto.edu/drorbn/AcademicPensieve/2012-01/thumbs/InfrastructureProject.png
How to use this site The Most Important Missing Infrastructure Project in Knot Theory
0:08:11 [edit] Correction (See discussion from around 0:43:40): Product in equation (2) of this blackboard shot should be from n to 1.
0:08:11 [add] Artin's theorem.
0:16:26 [add] McCool's Theorem.
0:16:26 [edit] It seems like (in the proof below): it has not been proven that the LHS contains the RHS. Addition: There should also be a version of Equation (2) in McCool's Theorem as in Artin's Theorem.
0:21:18 [add] Action by conjugation.
0:24:44 [edit] Time for a little exercise.
0:27:13 [add] The action of virtual crossings.
0:27:13 [edit] Correction: one too many strand on the right hand side.
0:41:48 [add] The action of real crossings.
0:41:55 [add] The action of real crossings (2).
0:46:50 [add] The action on the product of all generators.
0:49:32 [add] The action in the pure case.
0:54:57 [add] The "u" case.
0:59:40 [add] No semi-direct structure in the w case.
1:03:00 [add] The two actions of PvB_n.
1:07:40 [add] The two actions of PvB_n (2).