Taut foliations in surface bundles with multiple boundary components

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.

19 pages, 12 figures; Minor corrections made, corollary for contact structures included

References in corpus (3)

• Holomorphic disks and genus bounds
• Laminations and groups of homeomorphisms of the circle
• Laminar Branched Surfaces in 3-manifolds

Cited by in corpus (4)

• $C^0$ Approximations of foliations
• L-spaces, taut foliations and the Whitehead link
• Taut foliations from knot diagrams
• L-spaces, taut foliations and fibered hyperbolic two-bridge links