Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture

Abstract

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.

Updated and corrected following the comments of the referees. Final version to appear in "Geometry and Topology of Aspherical Manifolds", Contemp. Math. AMS. 28 pages and 3 figures