Quasi-isometries and the de Rham decomposition

We study quasi-isometries Phi:Pi X-i --> Pi 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. (C) 1998 Elsevier Science Ltd All rights reserved.