Quasi-isometries and the de Rham decomposition

Michael Kapovich, Bruce Kleiner, Bernhard Leeb

Research output: Contribution to journalArticle

Abstract

We study quasi-isometries Φ:∏Xi→∏Yj of product spaces and find conditions on the Xi,Yj 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.

Original languageEnglish (US)
Pages (from-to)1193-1211
Number of pages19
JournalTopology
Volume37
Issue number6
DOIs
StatePublished - Nov 1 1998

ASJC Scopus subject areas

  • Geometry and Topology

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