Volumes of hyperbolic Haken manifolds. I
type: Item
instance of: scholarly article
title: Volumes of hyperbolic Haken manifolds. I
zbMATH Open document ID: 0862.57008
DOI: 10.1007/BF01231535
author: Marc Culler
author: Peter B. Shalen
published in: Inventiones Mathematicae
publication date: 1994-12-18T00:00:00Z
full work available at URL: https://eudml.org/doc/144238
review text: The main result of this paper says that the volume of a closed hyperbolic 3-manifold \(M\) must exceed 0.34, provided it contains a non-separating surface whose complement is not a book of I-bundles. Using results from their previous work, the authors construct an open cover of the universal covering of \(M\) given by certain neighborhoods of the axis of hyperbolic elements of \(\pi_1M\). A very careful analysis reveals that this cover has combinatorial features which, under the assumption that \(\text{vol} (M)>0.34\) and that \(M\) contains a non-separating surface \(S\), imply that the complement of \(S\) must be a book of I-bundles.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 703870
zbMATH Keywords: volume
zbMATH Keywords: closed hyperbolic 3-manifold
zbMATH Keywords: universal covering
zbMATH Keywords: hyperbolic elements
reviewed by: Klaus Johannson
MaRDI profile type: Publication
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OpenAlex ID: W3158314511
description: scientific article; zbMATH DE number 703870