Local Floer homology and infinitely many simple Reeb orbits

Mark McLean

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let Q be a Riemannian manifold such that the Betti numbers of its free loop space with respect to some coefficient field are unbounded. We show that every contact form on its unit cotangent bundle supporting the natural contact structure has infinitely many simple Reeb orbits. This is an extension of a theorem by Gromoll and Meyer. We also show that if a compact manifold admits a Stein fillable contact structure then there is a possibly different such structure which also has infinitely many simple Reeb orbits for every supporting contact form. We use local Floer homology along with symplectic homology to prove these facts.

Original languageEnglish
Pages (from-to)1901–1923
Number of pages23
JournalAlgebraic & Geometric Topology
Volume12
Issue number4
DOIs
Publication statusPublished - 17 Sep 2012

Fingerprint

Contact Form
Floer Homology
Contact Structure
Orbit
Free Loop Space
Cotangent Bundle
Betti numbers
Compact Manifold
Riemannian Manifold
Homology
Unit
Coefficient
Theorem

Keywords

  • sympletic homology
  • local Floer
  • cotangent bundle
  • Reeb orbits

Cite this

Local Floer homology and infinitely many simple Reeb orbits. / McLean, Mark.

In: Algebraic & Geometric Topology, Vol. 12, No. 4, 17.09.2012, p. 1901–1923.

Research output: Contribution to journalArticle

McLean, Mark. / Local Floer homology and infinitely many simple Reeb orbits. In: Algebraic & Geometric Topology. 2012 ; Vol. 12, No. 4. pp. 1901–1923.
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