Realizing 4-manifolds as achiral Lefschetz fibrations

2005/09/30 by Etnyre, John B., Fuller, Terry · 2 citations
#57N13 #57R17 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.math/0510008

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.

Cited by

• A Simple Construction of Lefschetz Fibrations on Compact Stein Surfaces
• On totally symplectically aspherical manifolds

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