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

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

2001-09-20

arxiv.org/abs/math/0109150v1

Algebr. Geom. Topol. 1 (2001) 469-489

Mathematics

Symplectic Geometry

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-24.abs.html

Scientific paper

10.2140/agt.2001.1.469

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.

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