BNSR invariants and $\ell^2$-homology

Sam Hughes; Dawid Kielak

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arXiv · 2401.05545

BNSR invariants and $\ell^2$-homology

Sam Hughes·Dawid Kielak

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Abstract

We prove that if the $n$th $\ell^2$-Betti number of a group is non-zero then its $n$th BNSR invariant over $\mathbb{Q}$ 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.

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BibTeX RIS

Sam Hughes, Dawid Kielak. 2024-01-10. BNSR invariants and $\ell^2$-homology. https://arxiv.org/abs/2401.05545

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