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2012 Local Floer homology and infinitely many simple Reeb orbits
Mark McLean
Algebr. Geom. Topol. 12(4): 1901-1923 (2012). DOI: 10.2140/agt.2012.12.1901


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.


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Mark McLean. "Local Floer homology and infinitely many simple Reeb orbits." Algebr. Geom. Topol. 12 (4) 1901 - 1923, 2012.


Received: 8 February 2012; Revised: 19 June 2012; Accepted: 21 June 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1253.53078
MathSciNet: MR2994824
Digital Object Identifier: 10.2140/agt.2012.12.1901

Primary: 53D10, 53D25, 53D40

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 4 • 2012
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