Taut foliations in surface bundles with multiple boundary components

Tejas Kalelkar and Rachel Roberts

Vol. 273 (2015), No. 2, 257–275

DOI: 10.2140/pjm.2015.273.257

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.

Keywords

Dehn filling, taut foliation, fibered 3-manifold, contact structure, open book decomposition

Mathematical Subject Classification 2010

Primary: 57M50

Milestones

Received: 15 September 2013

Revised: 23 September 2013

Accepted: 27 September 2013

Published: 23 December 2014