Constructing broken Lefschetz fibrations from handle decompositions

TL;DR

This paper introduces a direct method for constructing broken Lefschetz fibrations from handle decompositions of 4-manifolds, providing explicit descriptions without relying on contact topology classifications.

Contribution

It presents a new handle-based approach to construct BLFs that works universally for doubles of 4-manifolds with boundary and includes explicit examples.

Findings

Method yields explicit BLF descriptions from handle decompositions.

Approach works for doubles of 4-manifolds with boundary.

Provides explicit BLFs on connected sums of S^2-bundles.

Abstract

We present an approach to constructing broken Lefschetz fibrations (BLFs) $f:X\rightarrow S^2$ from a handle decomposition of a 4-manifold $X$. Given a handle decomposition as input these techniques yield explicit descriptions of the BLFs, and do not rely on classification results from contact topology or the choice of a generic indefinite function like some earlier approaches. We show that this approach will always work in the case when $X$ is the double of a 4-manifold with boundary, and compute explicit examples of BLFs on connected sums of $S^2$-bundles.