The Maslov index as a quadratic space

Teruji Thomas
2006 Mathematical Research Letters  
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
more » ... sing elementary linear algebra. On the other hand, it has a nice interpretation in terms of sheaf cohomology, due to A. Beilinson.
doi:10.4310/mrl.2006.v13.n6.a13 fatcat:qvxvxeefuvfntjiodskvhrbvxa