2 problems

Let $n\geq 3$, let $\Gamma<\operatorname{SL}(n,{\bf R})$ be a lattice, and let $M$ be a compact manifold of dimension $n$. A volume-preserving blow-up or two-sided blow-up is one i…

Let $G$ be a semisimple Lie group with property $(T)$ and let $\Gamma$ be a lattice in $G$. Let $d$ be the least dimension of an infinite-image linear representation and $n$ the le…