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.
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