On homological properties of the Schlichting completion
arXiv:2406.12740 · doi:10.1017/S0305004125101357
Abstract
We show how finiteness properties of a group and a subgroup transfer to finiteness properties of the Schlichting completion relative to this subgroup. Further, we provide a criterion when the dense embedding of a discrete group into the Schlichting completion relative to one of its subgroups induces an isomorphism in (continuous) cohomology. As an application, we show that the continuous cohomology of the Neretin group vanishes in all positive degrees.
corrected formulation of Theorem 1.3