  In this paper, we construct a lax monoidal Topological Quantum Field Theory
that computes virtual classes, in the Grothendieck ring of algebraic varieties,
of $G$-representation varieties over manifolds with conic singularities, which
we will call nodefolds. This construction is valid for any algebraic group $G$,
in any dimension and also in the parabolic setting. In particular, this TQFT
allow us to compute the virtual classes of representation varieties over
complex singular planar curves. In addition, in the case $G =
\mathrm{SL}_{2}(k)$, the virtual class of the associated character variety over
a nodal closed orientable surface is computed both in the non-parabolic and in
the parabolic scenarios.
