Geometry & Topology

The Seiberg–Witten equations and the Weinstein conjecture II: More closed integral curves of the Reeb vector field

Clifford Henry Taubes

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Let M denote a compact, orientable 3–dimensional manifold and let a denote a contact 1–form on M; thus a da is nowhere zero. This article explains how the Seiberg–Witten Floer homology groups as defined for any given Spin structure on M give closed, integral curves of the vector field that generates the kernel of da.

Article information

Geom. Topol., Volume 13, Number 3 (2009), 1337-1417.

Received: 22 April 2007
Revised: 24 November 2008
Accepted: 1 December 2008
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 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]


Taubes, Clifford Henry. The Seiberg–Witten equations and the Weinstein conjecture II: More closed integral curves of the Reeb vector field. Geom. Topol. 13 (2009), no. 3, 1337--1417. doi:10.2140/gt.2009.13.1337.

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