Sam Hughes

collaborators

2 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.GR2023

Centralisers and the virtually cyclic dimension of $Out (F_{N})$

Yassine Guerch, Sam Hughes, Luis Jorge Sánchez Saldaña

We prove that the virtually cyclic (geometric) dimension of the finite index congruence subgroup $IA_{N} (3)$ of $Out (F_{N})$ is $2 N - 2$ . From this we deduce the virtua…

BNSR invariants and ℓ2-homology

Centralisers and the virtually cyclic dimension of Out(FN​)

BNSR invariants and $ℓ^{2}$ -homology

Centralisers and the virtually cyclic dimension of $Out (F_{N})$