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

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

2012-03-12

arxiv.org/abs/1203.2413v1

Mathematics

Geometric Topology

16 pages, 2 figures

Scientific paper

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 $\pi_1(M)$.

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