Geometry & Topology, Vol. 4 (2000) Paper no. 18, pages 517--535.

Symplectic Lefschetz fibrations on S^1 x M^3

Weimin Chen, Rostislav Matveyev

Abstract. 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.

Keywords. Four-manifold, symplectic structure, Lefschetz fibration, Seiberg-Witten invariants

AMS subject classification. Primary: 57M50. Secondary: 57R17, 57R57.

DOI: 10.2140/gt.2000.4.517

E-print: arXiv:math.DG/0002022

Submitted to GT on 12 April 2000. (Revised 8 December 2000.) Paper accepted 17 December 2000. Paper published 21 December 2000.

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Weimin Chen, Rostislav Matveyev
UW-Madison, Madison, WI 53706, USA
SUNY at Stony Brook, NY 11794, USA

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