  We prove the Singer conjecture for extended graph manifolds and pure
complex-hyperbolic higher graph manifolds with residually finite fundamental
groups. In real dimension three, where a result of Hempel ensures that the
fundamental group is always residually finite, we then provide a Price type
inequality proof of a well-known result of Lott and Lueck. Finally, we give
several classes of higher graph manifolds which do indeed have residually
finite fundamental groups.
