On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds
type: Item
instance of: scholarly article
title: On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds
zbMATH Open document ID: 0829.57006
DOI: 10.1007/BF01895833
author: Michael Kapovich
author: Bernhard Leeb
published in: Geometric and Functional Analysis. GAFA
publication date: 1996-01-15T00:00:00Z
full work available at URL: https://eudml.org/doc/58202
review text: The concept of asymptotic cone is applied to distinguish quasi-isometry classes of fundamental groups of 3-manifolds. It is proved that the existence of a Seifert component in a Haken manifold is a quasi-isometry invariant of its fundamental group. Results of this paper are used in the subsequent paper [the authors, Quasi-isometries preserve the geometric decomposition of Haken manifolds, Preprint, 1995] to prove quasi-isometry invariance of geometric decomposition of Haken manifolds and to describe finitely-generated groups which are quasi-isometric to fundamental groups of closed Haken 3-manifolds.
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 785235
zbMATH Keywords: quasi-isometry classes of fundamental groups of 3-manifolds
zbMATH Keywords: Seifert component
zbMATH Keywords: Haken manifold
zbMATH Keywords: geometric decomposition of Haken manifolds
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 785235