The Maslov cycle as a Legendre singularity and projection of a wavefront set

  title={The Maslov cycle as a Legendre singularity and projection of a wavefront set},
  author={Alan J. Weinstein},
  journal={Bulletin of the Brazilian Mathematical Society, New Series},
  • A. Weinstein
  • Published 2 July 2012
  • Mathematics
  • Bulletin of the Brazilian Mathematical Society, New Series
A Maslov cycle is a singular variety in the lagrangian grassmannian Λ(V) of a symplectic vector space V consisting of all lagrangian subspaces having nonzero intersection with a fixed one. Givental has shown that a Maslov cycle is a Legendre singularity, i.e. the projection of a smooth conic lagrangian submanifold S in the cotangent bundle of Λ(V). We show here that S is the wavefront set of a Fourier integral distributionwhich is “evaluation at 0 of the quantizations”. 
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