Quasi-isometries and the de Rham decomposition (Q1292651)

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.