The Maslov Gerbe
Abstract
Let Lag(E) be the grassmannian of lagrangian subspaces of a complex symplectic vector space E. We construct a Maslov class which generates the second integral cohomology of Lag(E), and we show that its mod 2 reduction is the characteristic class of a flat gerbe with structure group Z2. We explain the relation of this gerbe to the well-known flat Maslov line bundle with structure group Z4 over the real lagrangian grassmannian, whose characteristic class is the mod 4 reduction of the real Maslov class.
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