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

@article{Weinstein2012TheMC,
  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},
  year={2012},
  volume={44},
  pages={593-610}
}
  • 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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References

SHOWING 1-10 OF 19 REFERENCES
Connections of Berry and Hannay type for moving Lagrangian submanifolds
The category of Fresnel kernels
Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems
Let I be an open interval, M be a real manifold, T*M its cotangent bundle and \Phi={\phi_t}, t in I, a homogeneous Hamiltonian isotopy of T*M defined outside the zero-section. Let \Lambda be the
Lectures on Symplectic Manifolds
Introduction Symplectic manifolds and lagrangian submanifolds, examples Lagrangian splittings, real and complex polarizations, Kahler manifolds Reduction, the calculus of canonical relations,
The algebraic degree of semidefinite programming
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of
Fourier integral operators. I
Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value
Fourier integral operators. II
Symmetric Functions Schubert Polynomials and Degeneracy Loci
Introduction The ring of symmetric functions Schubert polynomials Schubert varieties A brief introduction to singular homology Bibliography Index.
The analysis of linear partial differential operators
the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certainproducts. Many products that you buy can be
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