Quantization of conic Lagrangian submanifolds of cotangent bundles
By St'ephane Guillermou. 2012
49 citations recorded by the source corpus.
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.
View Paper: https://www.semanticscholar.org/paper/4667be51c69e3c0f3f1b94119f88a30f92cb006e
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- Bohan Fang
Citations in the corpus
- Cluster varieties from Legendrian knots (2015, background): “lov’ obstruction to globalizing this equivalence. A trivialization loc() ˘=Loc() is determined by a Maslov potential on ; see [STZ] for a detailed discussion in the case where is one dimensional, or [Gui] for a general account. In this paper we generally do not consider front projections with cusps.”
- Microlocal Morse theory of wrapped Fukaya categories (2018, methodology): “It has been used on the sheaf side in [39, 60] to embed categories of microlocal sheaves into categories of (usual) sheaves, and we will use it for the same purpose here.”