Quasi-isometries and the de Rham decomposition

Michael Kapovich; Bruce Kleiner; Bernhard Leeb

doi:10.1016/S0040-9383(97)00091-8

Quasi-isometries and the de Rham decomposition

Michael Kapovich, Bruce Kleiner, Bernhard Leeb

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study quasi-isometries Φ:∏X_i→∏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.

Original language	English (US)
Pages (from-to)	1193-1211
Number of pages	19
Journal	Topology
Volume	37
Issue number	6
DOIs	https://doi.org/10.1016/S0040-9383(97)00091-8
State	Published - Nov 1 1998

ASJC Scopus subject areas

Geometry and Topology

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Quasi-isometries and the de Rham decomposition

Abstract

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