Convex plumbings and Lefschetz fibrations

TL;DR

This paper demonstrates that certain plumbings of symplectic surfaces in 4-manifolds can be equipped with convex neighborhoods that admit Lefschetz fibrations, aiding in symplectic topology constructions.

Contribution

It establishes conditions under which symplectic surface plumbings have convex neighborhoods that support Lefschetz fibrations and open book decompositions.

Findings

Convex neighborhoods exist under specific hypotheses.

Lefschetz fibrations can be constructed on these neighborhoods.

Applications to symplectic 4-manifold constructions are provided.

Abstract

We show that under appropriate hypotheses, a plumbing of symplectic surfaces in a symplectic 4-manifold admits strongly convex neighborhoods. Moreover the neighborhoods are Lefschetz fibered with an easily-described open book on the boundary supporting the induced contact structure. We point out some applications to cut-and-paste constructions of symplectic 4-manifolds.