Volume 9, issue 2 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
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