Small curvature laminations in hyperbolic 3–manifolds

Breslin, William

doi:10.2140/agt.2009.9.723

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Small curvature laminations in hyperbolic $3$–manifolds

William Breslin

Algebraic & Geometric Topology 9 (2009) 723–729

DOI: 10.2140/agt.2009.9.723

Abstract

We show that if $ℒ$ is a codimension-one lamination in a finite volume hyperbolic $3$ –manifold such that the principal curvatures of each leaf of $ℒ$ are all in the interval $(- δ, δ)$ for a fixed $δ$ with $0 \leq δ < 1$ and no complementary region of $ℒ$ is an interval bundle over a surface, then each boundary leaf of $ℒ$ has a nontrivial fundamental group. We also prove existence of a fixed constant $δ_{0} > 0$ such that if $ℒ$ is a codimension-one lamination in a finite volume hyperbolic $3$ –manifold such that the principal curvatures of each leaf of $ℒ$ are all in the interval $(- δ_{0}, δ_{0})$ and no complementary region of $ℒ$ is an interval bundle over a surface, then each boundary leaf of $ℒ$ has a noncyclic fundamental group.

Keywords

hyperbolic manifold, lamination

Mathematical Subject Classification 2000

Primary: 57M50

References

Publication

Received: 9 February 2009

Revised: 6 March 2009

Accepted: 8 March 2009

Published: 20 April 2009

Authors

William Breslin
Department of Mathematics University of Michigan 530 Church Street Ann Arbor 48109-1043 United States
http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=breslin

Volume 9, issue 2 (2009)