Quantization of conic Lagrangian submanifolds of cotangent bundles

Abstract

Let $M$ be a manifold and $\Lambda$ a compact exact connected Lagrangian submanifold of $T^{\ast }M$. We can associate with $\Lambda$ a conic Lagrangian submanifold ${\Lambda }^{\prime }$ of $T^{\ast }(M\times R)$. We prove that there exists a canonical sheaf $F$ on $M\times R$ whose microsupport is ${\Lambda }^{\prime }$ 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.

106 pages, second version, vanishing of Maslov class added

References in corpus (2)

• On triangulated orbit categories
• Microlocal condition for non-displaceablility

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