Relative formality theorem and quantisation of coisotropic submanifolds

@article{Cattaneo2007RelativeFT,
  title={Relative formality theorem and quantisation of coisotropic submanifolds},
  author={A. Cattaneo and G. Felder},
  journal={Advances in Mathematics},
  year={2007},
  volume={208},
  pages={521-548}
}
We prove a relative version of Kontsevich's formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich's theorem if C=M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L∞-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to the deformation quantisation of coisotropic submanifolds are given. The proof uses a duality… Expand