Graph manifolds and taut foliations

Abstract

We examine the existence of foliations without Reeb components, taut foliations, and foliations with no S1 × S1 -leaves, among graph manifolds. We show that each condition is strictly stronger than its predecessor(s), in the strongest possible sense; there are manifolds admitting foliations of each type which do not admit foliations of the succeeding type(s). © 1997 J. differential geometry.