Geometry & Topology
- Geom. Topol.
- Volume 11, Number 4 (2007), 2075-2115.
Constructing Lefschetz-type fibrations on four-manifolds
We show how to construct broken, achiral Lefschetz fibrations on arbitrary smooth, closed, oriented 4–manifolds. These are generalizations of Lefschetz fibrations over the 2–sphere, where we allow Lefschetz singularities with the non-standard orientation as well as circles of singularities corresponding to round 1–handles. We can also arrange that a given surface of square 0 is a fiber. The construction is easier and more explicit in the case of doubles of 4–manifolds without 3– and 4–handles, such as the homotopy 4–spheres arising from nontrivial balanced presentations of the trivial group.
Geom. Topol., Volume 11, Number 4 (2007), 2075-2115.
First available in Project Euclid: 20 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
Secondary: 57R17: Symplectic and contact topology
Gay, David T; Kirby, Robion. Constructing Lefschetz-type fibrations on four-manifolds. Geom. Topol. 11 (2007), no. 4, 2075--2115. doi:10.2140/gt.2007.11.2075. https://projecteuclid.org/euclid.gt/1513799978