Mathematics – Geometric Topology
Scientific paper
2009-01-09
Mathematics
Geometric Topology
7 pages, 1 figure
Scientific paper
We show that if $\mathcal{L}$ is a codimension-one lamination in a finite volume hyperbolic 3-manifold such that the principal curvatures of each leaf of $\mathcal{L}$ are all in the interval $(-\delta ,\delta)$ for a fixed $\delta\in[0,1)$ and no complimentary region of $\mathcal{L}$ is an interval bundle over a surface, then each boundary leaf of $\mathcal{L}$ has a nontrivial fundamental group. We also prove existence of a fixed constant $\delta_0 > 0$ such that if $\mathcal{L}$ is a codimension-one lamination in a finite volume hyperbolic 3-manifold such that the principal curvatures of each leaf of $\mathcal{L}$ are all in the interval $(-\delta_0 ,\delta_0)$ and no complimentary region of $\mathcal{L}$ is an interval bundle over a surface, then each boundary leaf of $\mathcal{L}$ has a noncyclic fundamental group.
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