5 problems

Let $M$ be a locally symmetric space associated to a group $G$ without discrete series, equivalently of the form $M=K \backslash G/\Gamma$ with Euler characteristic zero. A finite…

Let $M$ be a closed connected manifold of dimension at least $6$ with fundamental group $G=\pi_1(M)\cong \mathbf{Z}^{n+1}$. Let $\mathbb{G}=\{G_k\}$ be a nested tower of finite-ind…

Let $f:Y\to X$ be a finite cover of a genus $g\geq 2$ surface. Define the simple closed curve homology of the cover by … Here $H_1(Y;\C)$ is the first homology of $Y$ with complex…

Let $\Sigma$ be an oriented surface of finite type, and let $\phi\in\operatorname{Mod}(\Sigma)$ be an infinite-order mapping class. The paper proves the corresponding assertion whe…

Let $\Sigma$ be a surface and let $\psi$ be a mapping class which is pseudo-Anosov when restricted to some connected subsurface of $\Sigma$. A finite cover is a covering map…