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arXiv · 1212.5818

Quantization of conic Lagrangian submanifolds of cotangent bundles

Stéphane Guillermou
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Abstract

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

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Stéphane Guillermou. 2015-01-24. Quantization of conic Lagrangian submanifolds of cotangent bundles. https://arxiv.org/abs/1212.5818

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