Lefschetz fibrations, complex structures and Seifert fibrations on S1 X M3
Abstract
We consider product 4--manifolds S1 X M, where M is a closed, connected and oriented 3-manifold. We prove that if S1 X M admits a complex structure or a Lefschetz or Seifert fibration, then the following statement is true: S1 X M admits a symplectic structure if and only if M fibers over S1, 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 X M.
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