Lefschetz fibrations, complex structures and Seifert fibrations on S1 × M3

Etgu, Tolga¹

¹Department of Mathematics, University of California at Berkeley, Berkeley CA 94720, USA

Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 469-489

Résumé

We consider product 4–manifolds S1 × M, where M is a closed, connected and oriented 3–manifold. We prove that if S1 × M admits a complex structure or a Lefschetz or Seifert fibration, then the following statement is true:

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 S1 × M.

Détail

DOI : 10.2140/agt.2001.1.469

Keywords: product 4–manifold, Lefschetz fibration, symplectic manifold, Seiberg–Witten invariant, complex surface, Seifert fibration

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