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arxiv: 1212.5818 · v2 · pith:NXMJH5GWnew · submitted 2012-12-23 · 🧮 math.SG · math.GT

Quantization of conic Lagrangian submanifolds of cotangent bundles

classification 🧮 math.SG math.GT
keywords lambdalagrangianconicsubmanifoldtimesalreadyassociatebundles
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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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