Branched surfaces and the simplest foliations of 3-manifolds

Sandra L. Shields

Vol. 177 (1997), No. 2, 305–327

DOI: 10.2140/pjm.1997.177.305

Abstract

The set of foliations carried by the same branched surface as a foliation f includes, but is not restricted to, the set of foliations sufficiently close to f. We show that a branched surface may be constructed to ensure that no foliation carried by it has more dead-end components than f. In particular, if f is taut, all foliations carried by the branched surface will be taut. We use the result to classify the foliations of closed 3-manifolds having the fewest number of dead-end components. We then develop an algorithm to determine a lower bound on the depth of a foliation in a given class.

Milestones

Received: 31 March 1995

Revised: 26 December 1995

Published: 1 February 1997