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G&T Monographs |
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Constructing Lefschetz-type fibrations on four-manifolds
David T Gay and Robion Kirby
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Geometry & Topology 11 (2007)
2075–2115
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Abstract
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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.
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Keywords
Lefschetz fibrations, round handles, open
book decompositions, Andrews–Curtis conjecture, Gluck
construction, achiral, near-symplectic forms
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Mathematical Subject Classification
Primary: 57M50
Secondary: 57R17
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Publication
Received: 2007
Revised: 2007
Accepted: 2007
Published: 15 October 2007
Proposed: Simon Donaldson
Seconded: Ronald J Stern, Ron Fintushel
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