Sam Hughes

collaborators

2 papers

math.GR2024

Non-vanishing unitary cohomology of low-rank integral special linear groups

Benjamin Brück, Sam Hughes, Dawid Kielak +1

We construct explicit finite-dimensional orthogonal representations $π_{N}$ of $SL_{N} (Z)$ for $N \in {3, 4}$ all of whose invariant vectors are trivial, and…

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…

Non-vanishing unitary cohomology of low-rank integral special linear groups

BNSR invariants and ℓ2-homology

BNSR invariants and $ℓ^{2}$ -homology