Quasi-isometries and the de Rham decomposition
type: Item
instance of: scholarly article
title: Quasi-isometries and the de Rham decomposition
zbMATH Open document ID: 0954.53027
DOI: 10.1016/S0040-9383(97)00091-8
author: Bruce Kleiner
author: Michael Kapovich
author: Bernhard Leeb
published in: Topology
publication date: 1999-09-02T00:00:00Z
review text: Authors'abstract: We study quasi-isometries \(\Phi:\prod X_i \to \prod Y_j\) of product spaces and find conditions on the \(X_i\), \(Y_j\) which guarantee that the product structure is preserved. The main result applies to universal covers of compact Riemannian manifolds with nonpositive sectional curvature. We introduce a quasi-isometry invariant notion of coarse rank for metric spaces which coincides with the geometric rank for universal covers of closed nonpositively curved manifolds. This shows that the geometric rank is a quasi-isometry invariant.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 1307803
zbMATH Keywords: product structure
zbMATH Keywords: nonpositive sectional curvature
zbMATH Keywords: quasi-isometry
MaRDI profile type: Publication
full work available at URL: s0040-9383(97)00091-8
OpenAlex ID: W1995230276
description: scientific article; zbMATH DE number 1307803