Volume 20, issue 6 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

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 (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.

Keywords
contact homology, Reeb flows, topological entropy, symplectic field theory
Mathematical Subject Classification 2010
Primary: 37B40, 53D35, 53D42, 37J05
References
Publication
Received: 18 August 2015
Revised: 14 November 2015
Accepted: 21 December 2015
Published: 21 December 2016
Proposed: Yasha Eliashberg
Seconded: Ciprian Manolescu, Leonid Polterovich
Authors
Marcelo R R Alves
Institut de Mathématiques
Université de Neuchâtel
Rue Emile-Argand 11
CH-2000 Neuchâtel
Switzerland