Realizing 4-manifolds as Achiral Lefschetz Fibrations
نویسنده
چکیده
We show that any 4-manifold, after surgery on a curve, admits an achiral Lefschetz fibration. In particular, if X is a simply connected 4-manifold we show that X#S × S and X#S×̃S both admit achiral Lefschetz fibrations. 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
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