The Flat Closing Problem

The Flat Closing Problem is the following 1993 question of Gromov: Let X be a proper CAT(0) space and Γ be a discrete group acting properly and co-compactly by isometries on X. Does the existence of a flat plane in X imply that Γ contains a copy of ZxZ?

We will show that this question has a negative answer. The counterexample arises from a 4-dimensional pseudo-Anosov homeomorphism whose mapping torus is a hyperbolic 5-manifold.