Facts and Dreams About v-Knots and Etingof-Kazhdan
April-07-11
12:17 PM
Minutes
Topic
8
The Peter Lee setup for R,I, "all interesting graded equations arise in this way".
3
Example: the pure braid group (mention PvB, too).
3
Generalized algebraic structures.
1
Example: quandles.
4
Example: parenthesized braids and horizontal associators.
6
Example: KTGs and non-horizontal associators. ("Bracket rise" arises here).
5
Example: wKO's and the Kashiwara-Vergne equations.
15
vKO's, bi-algebras, E-K, what would it mean to find an expansion, why I care (stronger invariant, more interesting quotients).
5
wKO's, uKO's, and Alekseev-Enriquez-Torrosian.
1
The third page.
51
Total.
Abstract. I will describe, to the best of my understanding, the relationship between virtual knots and the Etingof-Kazhdan quantization of Lie bialgebras, and explain why, in my humble opinion, both topologists and algebraists should care. I am not happy yet about the state of my understanding of the subject but I haven't lost hope of achieving happiness, one day.