Quantization of conic Lagrangian submanifolds of cotangent bundles

Stéphane Guillermou

Quantization of conic Lagrangian submanifolds of cotangent bundles

Symplectic Geometry 2015-01-27 v2 Geometric Topology

Authors: Stéphane Guillermou

Abstract

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.

Keywords

quantization lagrangian submanifolds cotangent bundles microsupport maslov class sheaf theory symplectic geometry

Cite

@article{arxiv.1212.5818,
  title  = {Quantization of conic Lagrangian submanifolds of cotangent bundles},
  author = {Stéphane Guillermou},
  journal= {arXiv preprint arXiv:1212.5818},
  year   = {2015}
}

Comments

106 pages, second version, vanishing of Maslov class added

Quantization of conic Lagrangian submanifolds of cotangent bundles

Abstract

Keywords

Cite

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