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2001 Lefschetz fibrations, complex structures and Seifert fibrations on $S^1 \times M^3$
Tolga Etgu
Algebr. Geom. Topol. 1(1): 469-489 (2001). DOI: 10.2140/agt.2001.1.469

Abstract

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:

S1×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×M.

Citation

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Tolga Etgu. "Lefschetz fibrations, complex structures and Seifert fibrations on $S^1 \times M^3$." Algebr. Geom. Topol. 1 (1) 469 - 489, 2001. https://doi.org/10.2140/agt.2001.1.469

Information

Received: 7 August 2001; Accepted: 6 September 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0977.57010
MathSciNet: MR1852768
Digital Object Identifier: 10.2140/agt.2001.1.469

Subjects:
Primary: 57M50, 57R17, 57R57
Secondary: 32Q55, 53C15

Rights: Copyright © 2001 Mathematical Sciences Publishers

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