#### Volume 20, issue 6 (2016)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Cylindrical contact homology and topological entropy

### Marcelo R R Alves

Geometry & Topology 20 (2016) 3519–3569
##### 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 $\left(M,\xi \right)$ admits a hypertight contact form ${\lambda }_{0}$ for which the cylindrical contact homology has exponential homotopical growth rate, then the Reeb flow of every contact form on $\left(M,\xi \right)$ 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.

##### Keywords
contact homology, Reeb flows, topological entropy, symplectic field theory
##### Mathematical Subject Classification 2010
Primary: 37B40, 53D35, 53D42, 37J05