Journal of Symplectic Geometry

Volume 14 (2016)

Number 1

Topological complexity of symplectic 4-manifolds and Stein fillings

Pages: 171 – 202

DOI: http://dx.doi.org/10.4310/JSG.2016.v14.n1.a7

Authors

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

Jeremy Van Horn-Morris (Department of Mathematical Sciences, University of Arkansas, Fayetteville, Ark., U.S.A.)

Abstract

We prove that there exists no a priori bound on the Euler characteristic of a closed symplectic 4-manifold coming solely from the genus of a compatible Lefschetz pencil on it, nor is there a similar bound for Stein fillings of a contact 3-manifold coming from the genus of a compatible open book—except possibly for a few low genera cases. To obtain our results, we produce the first examples of factorizations of a boundary parallel Dehn twist as arbitrarily long products of positive Dehn twists along non-separating curves on a fixed surface with boundary. This solves an open problem posed by Auroux, Smith and Wajnryb, and a more general variant of it raised by Korkmaz, Ozbagci and Stipsicz, independently.

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article revised: 27 June 2016