8 problems

General semisimple-group conjecture. Theorems on the contractions and product structure—and consequently the orientability theorem and the relative-homology corollary—hold for any…

Let $X$ be a stratified space with stratification ${\cal S}$, let ${\cal P}(X,{\cal S})$ denote MacPherson's category of perverse sheaves, and let $D^b_{\cal S}(X)$ denote the boun…

Let $\mathcal{S}\mathrm{trat}$ denote a homotopy theory of topological stratified spaces, and let $\iCat$ denote the homotopy theory of $\infty$-categories. The exit path construct…

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 $M$ be a smooth manifold with a proper action of a group $G$. For each $x\in M$, let $N_x(M,G\cdot x)$ be the normal space to the orbit through $x$, and define … Let $G_x$ be t…

Categorical compactness conjecture. If $(X,P)$ is of finite stratified type, then $(X,P)$ is also categorically compact.

Let $f:X\to Y$ be a cylindrically stratified morphism of stratified topological spaces. A morphism is compactifiable if it factors as a stratified open embedding followed by a prop…