## Geometry & Topology

### Cylindrical contact homology and topological entropy

Marcelo Alves

#### Abstract

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

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

Dates
Revised: 14 November 2015
Accepted: 21 December 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859089

Digital Object Identifier
doi:10.2140/gt.2016.20.3519

Mathematical Reviews number (MathSciNet)
MR3590356

Zentralblatt MATH identifier
1362.37041

#### Citation

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

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