• Corpus ID: 118096304

Quantization of conic Lagrangian submanifolds of cotangent bundles

  title={Quantization of conic Lagrangian submanifolds of cotangent bundles},
  author={St'ephane Guillermou},
  journal={arXiv: Symplectic Geometry},
Let $M$ be a manifold and $\Lambda$ a compact exact connected Lagrangian submanifold of $T^*M$. We can associate with $\Lambda$ a conic Lagrangian submanifold $\Lambda'$ of $T^*(M\times R)$. We prove that there exists a canonical sheaf $F$ on $M\times R$ whose microsupport is $\Lambda'$ outside the zero section. We deduce the already known results that the Maslov class of $\Lambda$ is $0$ and that the projection from $\Lambda$ to $M$ induces isomorphisms between the homotopy groups. 
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