Symplectic homology and periodic orbits near symplectic submanifolds

Kai Cieliebak, Viktor L. Ginzburg, Ely Kerman

Research output: Contribution to journalArticlepeer-review

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. Mathematics Subject Classification (2000). 53D40, 37J45.

Original languageEnglish (US)
Pages (from-to)554-581
Number of pages28
JournalCommentarii Mathematici Helvetici
Volume79
Issue number3
DOIs
StatePublished - 2004
Externally publishedYes

Keywords

  • Hamiltonian flows
  • Periodic orbits
  • Symplectic homology
  • Symplectic submanifolds

ASJC Scopus subject areas

  • Mathematics(all)

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