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Let $M$ be a manifold and $\Lambda$ a compact exact connected Lagrangiansubmanifold of $T^*M$. We can associate with $\Lambda$ a conic Lagrangiansubmanifold $\Lambda'$ of $T^*(M\times R)$. We prove that there exists acanonical sheaf $F$ on $M\times R$ whose microsupport is $\Lambda'$ outside thezero section. We deduce the already known results that the Maslov class of$\Lambda$ is $0$ and that the projection from $\Lambda$ to $M$ inducesisomorphisms between the homotopy groups.

Quantization of conic Lagrangian submanifolds of cotangent bundles