Encoding 3 manifolds by planar graphs and computing perturbative invariants by counting planar subgraphs

par Michael Polyak (Technion)

vendredi 10 oct. 2025, 16:00 → 17:00 Europe/Paris

Fokko du Cloux (Bat. Braconnier)

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 has an interesting algebraic structure (being related to Lie algebras and braided ribbon Hopf algebras) and seems to be well-suited for
computation of perturbative invariants. While in the usual setup such invariants are given by complicated Feynman integrals over configuration spaces, in this case they turn into a simple weighted count of certain
subgraphs. We describe simplest invariants obtained in this way and propose a general theory of finite type invariants.