Dawid Kielak

activity

20212024

collaborators

3 papers

math.GT2024

BNSR invariants and $ℓ^{2}$ -homology

Sam Hughes, Dawid Kielak

We prove that if the $n$ th $ℓ^{2}$ -Betti number of a group is non-zero then its $n$ th BNSR invariant over $Q$ is empty, under suitable finiteness conditions. We apply thi…

math.GT2023

Coboundary expansion and Gromov hyperbolicity

Dawid Kielak, Piotr W. Nowak

We prove that if a compact $n$ -manifold admits a sequence of residual covers that form a coboundary expander in dimension $n - 2$ , then the manifold has Gromov-hyperbolic fundamental…

math.GT2021

Agrarian and $ℓ^{2}$ -Betti numbers of locally indicable groups, with a twist

Dawid Kielak, Bin Sun

We prove that twisted $ℓ^{2}$ -Betti numbers of locally indicable groups are equal to the usual $ℓ^{2}$ -Betti numbers rescaled by the dimension of the twisting representation; thi…

BNSR invariants and ℓ2-homology

Coboundary expansion and Gromov hyperbolicity

Agrarian and ℓ2-Betti numbers of locally indicable groups, with a twist

BNSR invariants and $ℓ^{2}$ -homology

Agrarian and $ℓ^{2}$ -Betti numbers of locally indicable groups, with a twist