Journal of Symplectic Geometry

Volume 14 (2016)

Number 3

Inequivalent Lefschetz fibrations and surgery equivalence of symplectic 4-manifolds

Pages: 671 – 686

DOI: http://dx.doi.org/10.4310/JSG.2016.v14.n3.a2

Author

R. İnanç Baykur (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Mass., U.S.A.)

Abstract

We prove that any symplectic 4-manifold which is not a rational or ruled surface, after sufficiently many blow-ups, admits an arbitrary number of nonisomorphic Lefschetz fibrations of the same genus which cannot be obtained from one another via Luttinger surgeries. This generalizes results of Park and Yun who constructed pairs of nonisomorphic Lefschetz fibrations on knot surgered elliptic surfaces. In turn, we prove that there are monodromy factorizations of Lefschetz pencils which have the same characteristic numbers but cannot be obtained from each other via partial conjugations by Dehn twists, answering a problem posed by Auroux.

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