Cylindrical contact homology and topological entropy

Alves, Marcelo¹

¹ Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, CH-2000 Neuchâtel, Switzerland

Geometry & topology, Tome 20 (2016) no. 6, pp. 3519-3569.

Résumé

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.

Détail

DOI : 10.2140/gt.2016.20.3519

Classification : 37B40, 53D35, 53D42, 37J05
Keywords: contact homology, Reeb flows, topological entropy, symplectic field theory

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