Hokkaido Mathematical Journal

JANECZKO S, MIKOSZ M,

On geometric properties of Lagrangian submanifolds in product symplectic spaces.

Hokkaido Mathematical Journal, 35 (2006) pp.215-227

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Abstract

We study the generic properties of symplectic relations. Local models of symplectic relations are described and the corresponding local symplectic invariants are derived. A stratification of the Lagrangian Grassmannian in the product symplectic space $(N\x M,\pi _M^*\w _M-\pi _N^*\w _N)$ is constructed and global homological properties of the strata are investigated.

MSC(Primary)58F05
MSC(Secondary)70H15, 57R45, 32S20
Uncontrolled Keywordssymplectic relation, Lagrangian Grassmannian, Maslov class