Trivalent graphs as an approach to Witten's asymptotics conjecture
by
Dylan Thurston
Harvard University

Witten's asymptotics conjecture says that the asymptotics of quantum invariants of a 3-manifold as the level goes to infinity are expressible as a sum over flat connections on the manifold. There are versions suitable for links, as well. In this talk we propose to extend the conjecture to knotted trivalent graphs and to prove some good behaviour under local moves. Since these local moves suffice to generate all knotted trivalent graphs, this would reduce the proof of the conjecture to just one case, an unknotted tetrahedron.

Date received: March 20, 2002