A note on the tameness of hyperbolic 3-manifolds
type: Item
instance of: scholarly article
title: A note on the tameness of hyperbolic 3-manifolds
zbMATH Open document ID: 1065.57018
author: Juan Souto
published in: Topology
publication date: 2005-03-08T00:00:00Z
review text: The tameness conjecture asserts that a hyperbolic 3-manifold with finitely generated fundamental group is tame (i.e. it is homeomorphic to the interior of a hyperbolic manifold with boundary). The paper under review proves a particular case of this conjecture. At the moment of writing this review, two independent proofs of the conjecture are available as preprints; both of them relying on the results or the ideas of this paper. One of the cases of the conjecture proved here involves ends having a sequence of surfaces converging to the end, such that the surfaces have bounded Euler characteristic and are incompressible in the exterior of a compact core. Recall that the inclusion of a compact core in the whole manifold is required to be a homotopy equivalence. This implies the conjecture when the manifold is a nested union of compact cores.
reviewed by: Joan Porti
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 2142206
zbMATH Keywords: hyperbolic manifolds
zbMATH Keywords: almost compact manifolds
zbMATH Keywords: tameness conjecture
MaRDI profile type: Publication
full work available at URL: j.top.2004.09.001
OpenAlex ID: W2005981560
DOI: 10.1016/J.TOP.2004.09.001
description: scientific article; zbMATH DE number 2142206