Geodesic
Symplectic Lefschetz fibrations on S1 × M3
Chen, Weimin1 ; Matveyev, Rostislav2
1 University of Wisconsin at Madison, Madison, Wisconsin 53706, USA
2 SUNY at Stony Brook, Stony Brook, New York 11794, USA
Geometry & topology, Tome 4 (2000) no. 1, pp. 517-535.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2000.4.517
Keywords: 4–manifold, symplectic structure, Lefschetz fibration, Seiberg–Witten invariants

Chen, Weimin 1 ; Matveyev, Rostislav 2

1 University of Wisconsin at Madison, Madison, Wisconsin 53706, USA
2 SUNY at Stony Brook, Stony Brook, New York 11794, USA 
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Chen, Weimin; Matveyev, Rostislav. Symplectic Lefschetz fibrations on S1 × M3. Geometry & topology, Tome 4 (2000) no. 1, pp. 517-535. doi : 10.2140/gt.2000.4.517. http://geodesic.mathdoc.fr/articles/10.2140/gt.2000.4.517/

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