Geometry & Topology

Constructing Lefschetz-type fibrations on four-manifolds

David T Gay and Robion Kirby

Full-text: Open access

Abstract

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.

Article information

Source
Geom. Topol., Volume 11, Number 4 (2007), 2075-2115.

Dates
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799978

Digital Object Identifier
doi:10.2140/gt.2007.11.2075

Mathematical Reviews number (MathSciNet)
MR2350472

Zentralblatt MATH identifier
1135.57009

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57R17: Symplectic and contact topology

Keywords
Lefschetz fibrations round handles open book decompositions Andrews–Curtis conjecture Gluck construction achiral near-symplectic forms

Citation

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


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