Actions of discrete groups on nonpositively curved spaces
type: Item
instance of: scholarly article
title: Actions of discrete groups on nonpositively curved spaces
zbMATH Open document ID: 0856.20024
DOI: 10.1007/BF01445254
author: Michael Kapovich
author: Bernhard Leeb
published in: Mathematische Annalen
publication date: 1997-02-12T00:00:00Z
full work available at URL: https://eudml.org/doc/165457
review text: This note contains several observations concerning discrete groups of non-parabolic isometries of spaces of nonpositive curvature. We prove that (almost all) surface mapping class groups do not admit such actions; in particular, they do not act cocompactly. A new obstruction to the existence of a nonpositively curved metric on closed manifolds is presented. We give examples of 4-manifolds fibered over surfaces and of graph 3-manifolds fibered over the circle which do not admit metrics of nonpositive curvature.
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 51K10
zbMATH DE Number: 952634
zbMATH Keywords: groups of isometries
zbMATH Keywords: mapping class groups
zbMATH Keywords: actions
zbMATH Keywords: nonpositively curved metrics
zbMATH Keywords: closed manifolds
MaRDI profile type: Publication
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OpenAlex ID: W2027034711
description: scientific article; zbMATH DE number 952634