Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture

Fuente: arXiv
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Main Authors: Di Cerbo, Luca F., Hull, Michael
Format: Preprint
Published: 2021
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author Di Cerbo, Luca F.
Hull, Michael
author_facet Di Cerbo, Luca F.
Hull, Michael
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2108_09236
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture
Di Cerbo, Luca F.
Hull, Michael
Differential Geometry
Geometric Topology
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.
title Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture
topic Differential Geometry
Geometric Topology
url https://arxiv.org/abs/2108.09236