BNSR invariants and $\ell^2$-homology
Geometric Topology
2024-01-12 v1 Algebraic Topology
Functional Analysis
Group Theory
K-Theory and Homology
Abstract
We prove that if the th -Betti number of a group is non-zero then its th BNSR invariant over is empty, under suitable finiteness conditions. We apply this to answer questions of Friedl--Vidussi and Llosa Isenrich--Py about aspherical K\"ahler manifolds, to verify some cases of the Singer Conjecture, and to compute certain BNSR invariants of poly-free and poly-surface groups.
Keywords
Cite
@article{arxiv.2401.05545,
title = {BNSR invariants and $\ell^2$-homology},
author = {Sam Hughes and Dawid Kielak},
journal= {arXiv preprint arXiv:2401.05545},
year = {2024}
}
Comments
31 pages, comments welcome!