Geometry & Topology 11 (2007) 2075–2115

DOI: 10.2140/gt.2007.11.2075

arXiv: math.GT/0701084

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.

Keywords

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

Mathematical Subject Classification

Primary: 57M50

Secondary: 57R17

References

Forward citations

Publication

Received: 2007
Revised: 2007
Accepted: 2007
Published: 15 October 2007
Proposed: Simon Donaldson
Seconded: Ronald J Stern, Ron Fintushel

Authors