Ring Around the Rosie

Embedded Trivalent Graphs and an Infant Conjecture

Bay Area Topology Seminar, Berkeley, February 15, 2000

Dror Bar-Natan1, Hebrew University and MSRI.

Abstract: Taking our motivation from the Chern-Simons-Witten expectations for the asymptotics of the Reshetikhin-Turaev invariants, we will state (in very simple terms) an infant conjecture about some well-behaved measure-valued invariant of embedded trivalent graphs. We will explain how our conjecture could be relevant for the realization of the Chern-Simons-Witten expectations, and how our conjecture can be reduced to the existence of a special invariant measure on some three copies of any given compact Lie group. Finally we will show that in some perturbative sense, our conjecture is true and in fact equivalent to Drinfel'd's theory of associators.

1Joint work with Dylan Thurston, who should not be held liable for all that will not make sense.

Hour Glass

This abstract is at http://www.math.toronto.edu/~drorbn/Talks/UCB-000215/.