Geometry & Topology

Cylindrical contact homology and topological entropy

Marcelo Alves

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We establish a relation between the growth of the cylindrical contact homology of a contact manifold and the topological entropy of Reeb flows on this manifold. We show that if a contact manifold (M,ξ) admits a hypertight contact form λ0 for which the cylindrical contact homology has exponential homotopical growth rate, then the Reeb flow of every contact form on (M,ξ) has positive topological entropy. Using this result, we provide numerous new examples of contact 3–manifolds on which every Reeb flow has positive topological entropy.

Article information

Geom. Topol., Volume 20, Number 6 (2016), 3519-3569.

Received: 18 August 2015
Revised: 14 November 2015
Accepted: 21 December 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37B40: Topological entropy 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 53D42: Symplectic field theory; contact homology 37J05: General theory, relations with symplectic geometry and topology

contact homology Reeb flows topological entropy symplectic field theory


Alves, Marcelo. Cylindrical contact homology and topological entropy. Geom. Topol. 20 (2016), no. 6, 3519--3569. doi:10.2140/gt.2016.20.3519.

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