Witten-Reshetikhin-Turaev invariants for 3-manifolds from Lagrangian intersections in configuration spaces

Cristina Ana-Maria Anghel

Published 2021-04-05Version 1

In this paper we construct a topological model for the Witten-Reshetikhin-Turaev invariants for $3$-manifolds as graded intersection pairings of homology classes in configuration spaces. More precisely, for a fixed level $\cN \in \N$ we show that the level $\cN$ WRT invariant for a $3-$manifold is a state sum of Lagrangian intersections in a covering of a fixed configuration space in the punctured disk. This model brings a new perspective on the structure of the level $\cN$ Witten-Reshetikhin-Turaev invariant, showing that it is completely encoded by the intersection points between certain Lagrangian submanifolds in a fixed configuration space, with additional gradings which come from a particular choice of a local system.