Taut foliations in surface bundles with multiple boundary components

TL;DR

This paper demonstrates how fibered 3-manifolds with multiple boundary components admit taut foliations that extend over Dehn fillings, linking fiber structures to contact geometry and symplectic fillability.

Contribution

It establishes a method to produce taut foliations from fiber structures in multi-boundary 3-manifolds and shows their extension to closed manifolds, connecting to contact and symplectic topology.

Findings

Existence of taut foliations for a range of rational multislopes.

Extensions of these foliations to closed 3-manifolds via Dehn filling.

Implication that certain contact structures are weakly symplectically fillable.

Abstract

Let $M$ be a fibered 3-manifold with multiple boundary components. We show that the fiber structure of $M$ transforms to closely related transversely oriented taut foliations realizing all rational multislopes in some open neighborhood of the multislope of the fiber. Each such foliation extends to a taut foliation in the closed 3-manifold obtained by Dehn filling along its boundary multislope. The existence of these foliations implies that certain contact structures are weakly symplectically fillable.