Seminars "Combinatorics of invariants". Speaker: Michael Polyak (Technion)

We introduce a new combinatorial encoding of 3-manifolds by planar graphs and discuss its interrelations to other known descriptions of 3-manifolds, electric networks, and knots. This graph encoding seems to be well-suited for computation of perturbative invariants 3-manifolds.
While in the usual setup perturbative invariants are given by complicated Feynman integrals over configuration spaces, in our case they turn into a simple weighted count of subgraphs.
We describe simplest invariants obtained in this way.