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On geometric properties of Lagrangian submanifolds in product symplectic spaces. (English) Zbl 1117.57028
The authors construct a new stratification of the Lagrangian Grassmannian in a product linear symplectic space and investigate the generic properties of symplectic relations with respect to the canonical projections. They also compute the first homology group of the strata and find a cycle whose homology class is dual to the universal Maslov class of the Grassmannian $$\Lambda_{n+m}$$.
##### MSC:
 57R45 Singularities of differentiable mappings in differential topology 53D12 Lagrangian submanifolds; Maslov index 53D35 Global theory of symplectic and contact manifolds
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