On geometric quantization of $b$-symplectic manifolds
  We study a notion of pre-quantization for $b$-symplectic manifolds. We use it to construct a formal geometric quantization of $b$-symplectic manifolds equipped with Hamiltonian torus actions with nonzero modular weight. We show that these quantizations are finite dimensional $T$-modules. 
Victor Guillemin, Eva Miranda and Jonathan Weitsman
math.SG math-ph math.DG math.MP