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

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Alan Weinstein

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  1. Alan Weinstein
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Correspondence to Alan Weinstein.

Additional information

Research partially supported by NSF Grant DMS-0707137 and the France-Berkeley Fund.

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Weinstein, A. The Maslov cycle as a Legendre singularity and projection of a wavefront set. Bull Braz Math Soc, New Series 44, 593–610 (2013). https://doi.org/10.1007/s00574-013-0026-6

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  • DOI: https://doi.org/10.1007/s00574-013-0026-6

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