JournalscmhVol. 79 , No. 3DOI 10.1007/s00014-004-0814-0

Symplectic homology and periodic orbits near symplectic submanifolds

  • Kai Cieliebak

    Universität Augsburg, Germany
  • Viktor L. Ginzburg

    UC Santa Cruz, USA
  • Ely Kerman

    SUNY at Stony Brook, USA
Symplectic homology and periodic orbits near symplectic submanifolds cover

Abstract

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.