Goettingen April 27,28,29, 2010

Overall Abstract.I will discuss three types of knotted objects - the "u" type, for "usual", the "v" type, for "virtual", and the "w" type, for "welded", or "weakly virtual", or "warm up". I will then discuss an abstract and general yet rather simple machine that in a uniform manner associates to each such class of knotted objects a "combinatorics", and a "low algebra", and a "high algebra". The latter is high indeed - it is the theory of Drinfel'd associators in the u case, most likely it is the Etingof-Kazhdan theory of quantization of Lie bi-algebras in the v case, and it is the Kashiwara-Vergne theory of convolutions on Lie groups and algebras in the w case. Thus these three pieces of high algebra have a simple topological origin. And as on the level of topology u, v, and w are tied together, their respective high algebra theories are closely related, with some of these relationships clearly understood, and some that are yet to be explored.

## Day 1 |
## Day 2 |
## Day 3 |

Handout - G1.html, G.pdf Talk Video. |
Handout - G2.html, G.pdf Talk Video. |
Handout - 18C.html, 18C.pdf Talk Video. |

All Goettingen sources are in G.zip. The Luminy sources are at Talks: Luminy-1004.