When incompressible tori meet essential laminations

Mark Brittenham and Rachel Roberts

Vol. 190 (1999), No. 1, 21–40

DOI: 10.2140/pjm.1999.190.21

Abstract

We show that there is only one obstruction to isotoping an essential lamination ℒ in a 3-manifold M containing an essential torus T so that when both ℒ and M are split open along T, the resulting lamination ℒ|T is essential in the split open manifold M|T. This is the existence of a cylindrical component in ℒ. This generalizes previous results relating taut foliations and essential tori.

Milestones

Received: 1 December 1997

Published: 1 September 1999