Algebraic and Geometric Topology 1 (2001), paper no. 24, pages 469-489.

Lefschetz fibrations, complex structures and Seifert fibrations on S^1 X M^3

Tolga Etgu

Abstract. We consider product 4--manifolds S^1 X M, where M is a closed, connected and oriented 3-manifold. We prove that if S^1 X M admits a complex structure or a Lefschetz or Seifert fibration, then the following statement is true: S^1 X M admits a symplectic structure if and only if M fibers over S^1, under the additional assumption that M has no fake 3-cells. We also discuss the relationship between the geometry of M and complex structures and Seifert fibrations on S^1 X M.

Keywords. Product 4-manifold, Lefschetz fibration, symplectic manifold, Seiberg-Witten invariant, complex surface, Seifert fibration

AMS subject classification. Primary: 57M50, 57R17, 57R57. Secondary: 53C15, 32Q55.

DOI: 10.2140/agt.2001.1.469

E-print: arXiv:math.SG/0109150

Submitted: 7 August 2001. Accepted: 6 September 2001. Published: 9 September 2001.

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Tolga Etgu
Department of Mathematics
University of California at Berkeley
Berkeley, CA 94720, USA
Email: tolga@math.berkeley.edu

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