Existence of broken Lefschetz fibrations

By R. Baykur. 2008

53 citations recorded by the source corpus.

We prove that every closed oriented smooth 4-manifold X admits a broken Lefschetz fibration (aka singular Lefschetz fibration) over the 2-sphere. Given any closed orientable surface F of square zero in X, we can choose the fibration so that F is a fiber. Moreover, we can arrange it so that there is only one Lefschetz critical point when the Euler characteristic e(X) is odd, and none when e(X) is even. We make use of topological modifications of smooth maps with fold and cusp singularities due to Saeki and Levine, and thus we get alternative proofs of previous existence results. Also shown is the existence of broken Lefschetz pencils with connected fibers on any near-symplectic 4-manifold.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b2de22ae5f9e117a8830b944b5348701f92ab13e

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In Geometry and Topology

1. Yankı Lekili
2. R. Baykur
3. Nathan Sunukjian

In Mathematical Physics

1. Yankı Lekili
2. R. Baykur
3. Nathan Sunukjian

Citations in the corpus

• Wrinkled fibrations on near-symplectic manifolds (2007, methodology): “In [5] we gave a handlebody description of a broken Lefschetz fibration on CP as a counterexample to Gay and Kirby’s conjecture on the necessity of negative Lefschetz singularities for generalized fibrations on arbitrary 4–manifolds, and pointed out how this picture could be used to modify any given”
• Round handles, logarithmic transforms and smooth 4‐manifolds (2010, background): “These fibrations are found in abundance, as any generic map from X to S(2) can be homotoped to a broken Lefschetz fibration [15, 5].”