Hyperkähler metrics near Lagrangian submanifolds and symplectic groupoids

Lagrangian Submanifolds in Hyperkähler manifolds, Legendre transformation

Periodic Orbits near Symplectic Submanifolds

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...

Lagrangian submanifolds in product symplectic spaces

We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and investigate the local properties of generic symplectic relations. The cohomological symplectic invariant of discrete dynamical systems is generalized to the class of generalized canonical mappings. Lower bounds for the number of two-point and three-point symplectic invariants for billiard-type dynamic...

Symplectic Homology and Periodic Orbits near Symplectic Submanifolds

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...

On geometric properties of Lagrangian submanifolds in product symplectic spaces

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 ×M, π∗ MωM − π∗ NωN ) is constructed and global homological properties of the strata are investigated.