The Seiberg–Witten equations and the Weinstein conjecture

Taubes, Clifford Henry

doi:10.2140/gt.2007.11.2117

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The Seiberg–Witten equations and the Weinstein conjecture

Clifford Henry Taubes

Geometry & Topology 11 (2007) 2117–2202

DOI: 10.2140/gt.2007.11.2117

arXiv: math.SG/0611007

Abstract

Let $M$ denote a compact, oriented 3–dimensional manifold and let $a$ denote a contact 1–form on $M$ ; thus $a \land d a$ is nowhere zero. This article proves that the vector field that generates the kernel of $d a$ has a closed integral curve.

Keywords

Weinstein conjecture, vector field, contact form, 3-manifold

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 57R57

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Publication

Received: 14 January 2007

Accepted: 18 May 2007

Published: 15 October 2007

Proposed: Robion Kirby

Seconded: Tom Mrowka, Ron Fintushel

Authors

Clifford Henry Taubes
Department of Mathematics Harvard University Cambridge MA 02133

Volume 11, issue 4 (2007)