Symplectic homology and periodic orbits near symplectic submanifolds

Details Symplectic homology and periodic orbits near symplectic submanifolds Symplectic homology and periodic orbits near symplectic submanifolds

2002-10-30

arxiv.org/abs/math/0210468v2

Mathematics

Differential Geometry

21 pages, 1 figure. reference added

Scientific paper

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has non-vanishing 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 implies the existence of contractible periodic orbits for a dense set of low energy values.

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