2 problems

Let $\Gamma$ be an irreducible higher-rank lattice. Lubotzky's property $\tau$ conjecture. The group $\Gamma$ has property $\tau$. This is listed among consequences of the spectral…

Perfect-closure property $(\tau)$ conjecture. The group $\Gamma$ has property $(\tau)$ with respect to the family $\{\Gamma(I)\}$ as $I$ ranges over all finite-index ideals of $R$.…