© | Dror Bar-Natan: (Talks: SwissKnots-1105) / (Odds and Ends: Videos for Swiss Knots 2011):

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Videography by Peter Lee

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0:00:00 [add] Handout view 2: Abstract and Apology
0:01:04 [add] Handout view 3: Abstract Generalities
0:01:26 [add] Handout view 3: Abstract Generalities
0:06:34 [add] Handout view 4: Pure Braids
0:06:40 [add] Handout view 3: Abstract Generalities
0:07:53 [add] Handout view 4: Pure Braids
0:11:52 [add] Handout view 3: Abstract Generalities
0:11:57 [add] Handout view 4: Pure Braids
0:12:04 [add] Handout view 5: Why Prized?
0:12:55 [add] Handout view 4: Pure Braids
0:13:18 [add] Handout view 5: Why Prized?
0:13:57 [add] Handout view 6: Pure Virtual Braids
0:16:56 [add] Handout view 7: General Algebraic Structures
0:19:28 [add] Handout view 8: Quandles
0:19:28 [edit] A Leibniz algbera is a Lie algebra minus the anti-symmetry of the bracket; I have previously erroneously asserted that here {\mathcal A}(K) is Lie; however,

Jim,

Ooops, you are probably right and I should retract my claim and revert to the
older version, which just said that gr is a Leibniz algebra. Do you allow me to
post this conversation as is (minus your email address) as a reference? Where
did you find the Lie claim? I just made it now at Swiss Knots 2011, but I have
the feeling I made it elsewhere too.

Best,

Dror.

On Wed, 1 Jun 2011, James Conant wrote:

> Hi Dror,
>
> I know you must be busy, but I have a quick question about a claim on one of
> your slides that the quadratic approximation to the associated graded object
> for a quandle (with unit) is a (graded) Lie algebra. This caught my eye since
> I am on the look-out for interesting constructions of Lie algebras associated
> to knots and links. In any event, I haven't been able to prove antisymmetry.
> It's pretty obvious that on the basis {(v-1)} for the augmentation ideal that
> (v-1)^(v-1)=0. If we also knew that x^x=0 for arbitrary linear combinations
> of these basic v-1s, we'd be done, but I don't see how to show that. Perhaps
> I'm missing something obvious.
>
> Thanks,
>
> -Jim
0:20:11 [add] Handout view 9: Parenthesized Braids
0:25:31 [add] Handout view 10: Knotted Trivalent Graphs
0:27:55 [add] Handout view 11: Tetrahedron, Prizm, Pentagon
0:29:40 [add] Handout view 12: Diagrams and Tensors, 1
0:33:24 [add] Handout view 13: Ribbon 2-Knots
0:38:50 [add] Handout view 14: Trivalent w-Tangles
0:38:56 [add] Handout view 13: Ribbon 2-Knots
0:39:25 [add] Handout view 14: Trivalent w-Tangles
0:40:28 [add] Handout view 15: Alekseev-Torrosian-Kashiwara-Vergne
0:42:41 [add] Handout view 16: vTT and Av
0:44:14 [add] Handout view 17: Diagrams and Tensors, 2
0:45:12 [add] Handout view 18: The Forbidden Theorem
0:47:08 [add] Handout view 19: Why Shoyuld We Care?
0:47:24 [add] Handout view 18: The Forbidden Theorem
0:47:30 [add] Handout view 19: Why Shoyuld We Care?
0:51:58 [add] Handout view 20: V to Phi
0:52:30 [add] Handout view 21: Strands and Punctures
0:53:14 [add] Handout view 22: Phi to V
0:53:19 [add] Handout view 21: Strands and Punctures
0:53:23 [add] Handout view 22: Phi to V
0:53:38 [add] Handout view 23: Alexander is Easy
0:53:45 [add] Handout view 24: Many Kinds of Virtuals!
0:53:50 [add] Handout view 25: Help Needed!
0:54:03 [add] Handout view 26: Propaganda
0:54:30 [add] Handout view 2: Abstract and Apology