Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 1, Number 1 (2001), 469-489.
Lefschetz fibrations, complex structures and Seifert fibrations on $S^1 \times M^3$
We consider product 4–manifolds , where is a closed, connected and oriented 3–manifold. We prove that if admits a complex structure or a Lefschetz or Seifert fibration, then the following statement is true:
admits a symplectic structure if and only if fibers over ,
under the additional assumption that has no fake 3–cells. We also discuss the relationship between the geometry of and complex structures and Seifert fibrations on .
Algebr. Geom. Topol., Volume 1, Number 1 (2001), 469-489.
Received: 7 August 2001
Accepted: 6 September 2001
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds 57R17: Symplectic and contact topology 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 32Q55: Topological aspects of complex manifolds
Etgu, Tolga. Lefschetz fibrations, complex structures and Seifert fibrations on $S^1 \times M^3$. Algebr. Geom. Topol. 1 (2001), no. 1, 469--489. doi:10.2140/agt.2001.1.469. https://projecteuclid.org/euclid.agt/1513882604