3 problems

Let $X$ be a symmetric space of non-compact type. An arithmetic $X$-manifold is an arithmetic manifold locally modeled on $X$, and a family has uniform homotopy complexity if there…

Fix an arithmetic congruence hyperbolic $3$-manifold $M_0$. For any arithmetic congruence hyperbolic $3$-manifold $M\to M_0$ of volume $V$, let $H_2(M,\mathbb{R})$ denote its real…

Let $Y$ be the arithmetic manifold, let $E(\lambda)$ be the coefficient system, and let $H^{n\times q}_{\mathrm{cusp}}(Y,E(\lambda))$ denote the indicated cuspidal cohomology subsp…