Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture
Differential Geometry
2024-06-10 v4 Geometric Topology
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.
Keywords
Cite
@article{arxiv.2108.09236,
title = {Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture},
author = {Luca F. Di Cerbo and Michael Hull},
journal= {arXiv preprint arXiv:2108.09236},
year = {2024}
}
Comments
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