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

Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture