Realizing 4-manifolds as achiral Lefschetz fibrations

Details Realizing 4-manifolds as achiral Lefschetz fibrations Realizing 4-manifolds as achiral Lefschetz fibrations

2005-09-30

arxiv.org/abs/math/0510008v2

Mathematics

Geometric Topology

15 pages, 2 figures

Scientific paper

We show that any 4-manifold, after surgery on a curve, admits an achiral Lefschetz fibration. In particular, we show that the connected sum of any simply connected 4-manifold with a 2-sphere bundle over the 2-sphere will admit an achiral Lefschetz fibration. We also show these surgered manifolds admit near-symplectic structures and prove more generally that achiral Lefschetz fibrations with sections have near-symplectic structures. As a corollary to our proof we obtain an alternate proof of Gompf's result on the existence of symplectic structures on Lefschetz pencils.

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