Let
be a
fibered 3-manifold with multiple boundary components. We show that the fiber structure
of
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.
Keywords
Dehn filling, taut foliation, fibered 3-manifold, contact
structure, open book decomposition