Realizing 4-manifolds as achiral Lefschetz fibrations

John B. Etnyre; Terry Fuller

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arXiv · math/0510008

Realizing 4-manifolds as achiral Lefschetz fibrations

John B. Etnyre·Terry Fuller

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Abstract

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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BibTeX RIS

John B. Etnyre, Terry Fuller. 2006-01-22. Realizing 4-manifolds as achiral Lefschetz fibrations. https://arxiv.org/abs/math/0510008

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