Top degree \(\ell^{p}\)-homology and conformal dimension of buildings (Q6562925)

At the very beginning, buildings were introduced by Tits to show simplicity of some families of groups. Later, they are viewed as non-Archimedean analogues of symmetric spaces. They may also be viewed as metric spaces. In this paper, the authors consider the \(l^p\)-cohomology of these metric spaces. In fact, they are interested in top dimensional simplicial \(l^p\)-cohomology of buildings. In particular, for a non-compact finite thickness building whose Davis apartment is an orientable pseudo manifold, they compute the supremum of the set of \(p>1\) such that its top dimensional reduced \(l^p\)-cohomology is non-zero. Using Bestvina realisation, they generalise the results for any finite thickness building.