Commentarii Mathematici Helvetici

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Volume 79, Issue 3, 2004, pp. 554–581
DOI: 10.1007/s00014-004-0814-0

Published online: 2004-09-30

Symplectic homology and periodic orbits near symplectic submanifolds

Kai Cieliebak[1], Viktor L. Ginzburg[2] and Ely Kerman[3]

(1) Universit├Ąt Augsburg, Germany
(2) UC Santa Cruz, USA
(3) SUNY at Stony Brook, USA

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.

Keywords: periodic orbits, Hamiltonian flows, symplectic homology, symplectic submanifolds

Cieliebak Kai, Ginzburg Viktor, Kerman Ely: Symplectic homology and periodic orbits near symplectic submanifolds. Comment. Math. Helv. 79 (2004), 554-581. doi: 10.1007/s00014-004-0814-0