Geometry & Topology

Symplectic Lefschetz fibrations on $S^1 \times M^3$

Weimin Chen and Rostislav Matveyev

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In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-manifold with a circle admits a symplectic structure, then the three-manifold must fiber over a circle, and up to a self-diffeomorphism of the four-manifold, the symplectic structure is deformation equivalent to the canonical symplectic structure determined by the fibration of the three-manifold over the circle.

Article information

Geom. Topol., Volume 4, Number 1 (2000), 517-535.

Received: 12 April 2000
Revised: 8 December 2000
Accepted: 17 December 2000
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57R17: Symplectic and contact topology 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

4–manifold symplectic structure Lefschetz fibration Seiberg–Witten invariants


Chen, Weimin; Matveyev, Rostislav. Symplectic Lefschetz fibrations on $S^1 \times M^3$. Geom. Topol. 4 (2000), no. 1, 517--535. doi:10.2140/gt.2000.4.517.

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