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

Yosuke Kano

doi:10.2140/pjm.2014.267.399

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arXiv · 1203.2413

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

Yosuke Kano

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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 $\pi_1(M)$.

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BibTeX RIS

Yosuke Kano. 2012-03-12. Taut foliations and the actions of fundamental groups on leaf spaces and universal circles. https://doi.org/10.2140/pjm.2014.267.399

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