Lagrangian non-intersections
The paper under review presents some results concerning Lagrangian submanifolds of a symplectic manifold and their intersection patterns. Its results point out two phenomena. One of the phenomena is that in certain symplectic manifold the topology of Lagrangians with small first homology is extremely restricted. It turns out that in some cases certain assumptions on \(H_{1}(L,\mathbb{Z})\) of a Lagrangian \(L\) completely determine the entire homology of \(L\). The second phenomenon belongs to the framework of Lagrangian intersections. His results show that certain symplectic manifolds \(M\) contain some kind of ``Lagrangian core'' \(\Lambda\subset{M}\) which dominates intersections in the sense that many global Lagrangians \(L\subset{M}\) must intersect \(\Lambda\), the intersection points being irremovable by symplectic diffeomorphisms.
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