  Let $M$ be complete nonpositively curved Riemannian manifold of finite volume
whose fundamental group $\Gamma$ does not contain a finite index subgroup which
is a product of infinite groups. We show that the universal cover $\tilde M$ is
a higher rank symmetric space iff $H^2_b(M;\R)\to H^2(M;\R)$ is injective (and
otherwise the kernel is infinite-dimensional). This is the converse of a
theorem of Burger-Monod. The proof uses the celebrated Rank Rigidity Theorem,
as well as a new construction of quasi-homomorphisms on groups that act on
CAT(0) spaces and contain rank 1 elements.
