Hyperbolic 3-manifolds with nonintersecting closed geodesics
type: Item
instance of: scholarly article
title: Hyperbolic 3-manifolds with nonintersecting closed geodesics
zbMATH Open document ID: 1027.57018
DOI: 10.1023/A:1023657806258
author: Ara Basmajian
author: Scott A. Wolpert
published in: Geometriae Dedicata
publication date: 2003-08-06T00:00:00Z
review text: A complete (orientable) Riemannian manifold is said to have the spd-property if all its closed geodesics are simple and pairwise disjoint. In the paper under review, the spd-property is investigated for Riemannian \(3\)-manifolds which admit a geometrically finite hyperbolic structure. The authors prove that either the generic hyperbolic structure has the spd-property or no hyperbolic structure has it, and show that both situations occur. They analyze the case when the manifold is the interior of a handlebody or of the product of a surface with an interval of negative Euler characteristic and proof that, for these manifolds, the generic hyperbolic structure has the spd-property. Finally it is observed that having the spd-property is a commensurability invariant.
reviewed by: Luisa Paoluzzi
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 30F40
zbMATH DE Number: 1960053
zbMATH Keywords: hyperbolic manifold
zbMATH Keywords: Kleinian group
zbMATH Keywords: spd-property
MaRDI profile type: Publication
full work available at URL: a:1023657806258
OpenAlex ID: W206379196
description: scientific article; zbMATH DE number 1960053