Geometry & Topology
- Geom. Topol.
- Volume 20, Number 6 (2016), 3519-3569.
Cylindrical contact homology and topological entropy
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 admits a hypertight contact form for which the cylindrical contact homology has exponential homotopical growth rate, then the Reeb flow of every contact form on has positive topological entropy. Using this result, we provide numerous new examples of contact –manifolds on which every Reeb flow has positive topological entropy.
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
Permanent link to this document
Digital Object Identifier
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
Alves, Marcelo. Cylindrical contact homology and topological entropy. Geom. Topol. 20 (2016), no. 6, 3519--3569. doi:10.2140/gt.2016.20.3519. https://projecteuclid.org/euclid.gt/1510859089