  In this paper we construct a topological model for the
Witten-Reshetikhin-Turaev invariants for $3$-manifolds coming from the quantum
group $U_q(sl(2))$, 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 {\bf 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. This formula provides a new framework for
investigating the open question about categorifications of the WRT invariants.
