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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 infinitecyclic group generated by an indivisible element of $\pi_1(M)$.

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