1998/11/01 by Michael Kapovich, Bruce Kleiner, Bernhard Leeb
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · doi:10.1016/s0040-9383(97)00091-8
crossref issued 1998/11/01 · crossref published 1998/11/01 · crossref published-print 1998/11/01 · openalex publication_date 1998/11/01 · crossref created 2002/07/25 · crossref deposited 2025/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02 · crossref indexed 2026/07/29
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.