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The Maslov index as a quadratic space

2006
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Mathematical Research Letters
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Kashiwara defined the Maslov index (associated to a collection of Lagrangian subspaces of a symplectic vector space over a field F ) as a class in the Witt group W (F ) of quadratic forms. We construct a canonical quadratic vector space in this class and show how to understand the basic properties of the Maslov index without passing to W (F )-that is, more or less, how to upgrade Kashiwara's equalities in W (F ) to canonical isomorphisms between quadratic spaces. The quadratic space is defined

doi:10.4310/mrl.2006.v13.n6.a13
fatcat:qvxvxeefuvfntjiodskvhrbvxa