Constructing Lefschetz-type fibrations on four-manifolds

David T Gay, Robion Kirby
2007 Geometry and Topology  
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,
more » ... uch as the homotopy 4-spheres arising from nontrivial balanced presentations of the trivial group.
doi:10.2140/gt.2007.11.2075 fatcat:cjopsqgbdfadrgvcvgj276fpj4