6 problems

Let $D$ be the diagonal group of $\operatorname{SL}_n(\mathbb{R})$ where $n\ge 3$. A $D$-orbit in $\operatorname{SL}_n(\mathbb{R})/\operatorname{SL}_n(\mathbb{Z})$ is relatively co…

Let $X$ be a compact homogeneous manifold, let $f_0\in\operatorname{Aff}(X)$ be a $K$-system, and suppose that $\mathcal{Z}(f_0)$ contains a hyperbolic affine diffeomorphism. If…

Let $M$ be a Scott complex or quaternionic manifold with its natural stratification. Let $N$ be a stratified space and let $f:N\to M$ be a stratified homotopy equivalence. Stratifi…

Let $M^n$ be a manifold with a “nice” group action or a space with a “nice” stratification, and let $N^n$ be another manifold or space that is equivariantly or stratified homotopy…

Let ${\cal F}$ be a family of maps, and let $f\in{\cal F}$ be non-hyperbolic. The map $f$ is topologically rigid when it is not topologically conjugate to any other map in a suffic…

Let $M\to E\to B$ be a smooth fiber bundle whose fiber admits a negatively curved Riemannian metric. Assume that $B$ is a paracompact, Hausdorff space with the homotopy type of a s…