Open Access
Translator Disclaimer
2009 Small curvature laminations in hyperbolic $3$–manifolds
William Breslin
Algebr. Geom. Topol. 9(2): 723-729 (2009). DOI: 10.2140/agt.2009.9.723

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 0δ<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.

Citation

Download Citation

William Breslin. "Small curvature laminations in hyperbolic $3$–manifolds." Algebr. Geom. Topol. 9 (2) 723 - 729, 2009. https://doi.org/10.2140/agt.2009.9.723

Information

Received: 9 February 2009; Revised: 6 March 2009; Accepted: 8 March 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1178.57018
MathSciNet: MR2496887
Digital Object Identifier: 10.2140/agt.2009.9.723

Subjects:
Primary: 57M50

Rights: Copyright © 2009 Mathematical Sciences Publishers

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.9 • No. 2 • 2009
MSP