Volume 13, issue 2 (2009)

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

Volume 23
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

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
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
The Weinstein conjecture for stable Hamiltonian structures

Michael Hutchings and Clifford Henry Taubes

Geometry & Topology 13 (2009) 901–941
Abstract

We use the equivalence between embedded contact homology and Seiberg–Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3–manifold with a stable Hamiltonian structure, and let R denote the associated Reeb vector field on Y . We prove that if Y is not a T2–bundle over S1, then R has a closed orbit. Along the way we prove that if Y is a closed oriented connected 3–manifold with a contact form such that all Reeb orbits are nondegenerate and elliptic, then Y is a lens space. Related arguments show that if Y is a closed oriented 3–manifold with a contact form such that all Reeb orbits are nondegenerate, and if Y is not a lens space, then there exist at least three distinct embedded Reeb orbits.

Keywords
dynamical system, Seiberg–Witten, Floer homology
Mathematical Subject Classification 2000
Primary: 57R17, 57R57, 53D40
Secondary: 57R58
References
Publication
Received: 21 September 2008
Revised: 8 December 2008
Accepted: 20 November 2008
Published: 8 January 2200
Proposed: Yasha Eliashberg
Seconded: Peter Ozsvath, Leonid Polterovich
Authors
Michael Hutchings
Mathematics Department
970 Evans Hall
University of California
Berkeley, CA 94720
USA
Clifford Henry Taubes
Mathematics Department
Harvard University
Cambridge, MA 02138
USA