Taut foliations and the actions of fundamental groups on leaf spaces and universal circles

Abstract

Let $F$ be a leafwise hyperbolic taut foliation of a closed 3-manifold $M$ and let $L$ be the leaf space of the pullback of $F$ to the universal cover of $M$. We show that if $F$ has branching, then the natural action of ${\pi }_1(M)$ on $L$ is faithful. We also show that if $F$ has a finite branch locus $B$ whose stabilizer acts on $B$ nontrivially, then the stabilizer is an infinite cyclic group generated by an indivisible element of ${\pi }_1(M)$.

16 pages, 2 figures

References in corpus (2)

• Laminations and groups of homeomorphisms of the circle
• Centralizers in 3-manifold groups