The Maslov cycle as a Legendre singularity and projection of a wavefront set
Symplectic Geometry
2012-07-03 v1
Abstract
A Maslov cycle is a singular variety in the lagrangian grassmannian L(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 L(V). We show here that S is the wavefront set of a Fourier integral distribution which is "evaluation at 0 of the quantizations".
Keywords
Cite
@article{arxiv.1207.0408,
title = {The Maslov cycle as a Legendre singularity and projection of a wavefront set},
author = {Alan Weinstein},
journal= {arXiv preprint arXiv:1207.0408},
year = {2012}
}