Geometry & Topology

The Seiberg–Witten equations and the Weinstein conjecture

Clifford Henry Taubes

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

Article information

Geom. Topol., Volume 11, Number 4 (2007), 2117-2202.

Received: 14 January 2007
Accepted: 18 May 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology
Secondary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

Weinstein conjecture vector field contact form 3-manifold


Taubes, Clifford Henry. The Seiberg–Witten equations and the Weinstein conjecture. Geom. Topol. 11 (2007), no. 4, 2117--2202. doi:10.2140/gt.2007.11.2117.

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