Volume 9, issue 2 (2009)

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Small curvature laminations in hyperbolic $3$–manifolds

William Breslin

Algebraic & Geometric Topology 9 (2009) 723–729
Abstract

We show that if is a codimension-one lamination in a finite volume hyperbolic 3–manifold such that the principal curvatures of each leaf of are all in the interval (δ,δ) for a fixed δ with 0 δ < 1 and no complementary region of is an interval bundle over a surface, then each boundary leaf of has a nontrivial fundamental group. We also prove existence of a fixed constant δ0 > 0 such that if is a codimension-one lamination in a finite volume hyperbolic 3–manifold such that the principal curvatures of each leaf of are all in the interval (δ0,δ0) and no complementary region of is an interval bundle over a surface, then each boundary leaf of 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