5 problems

Resolution conjecture. Every generalized $n$-manifold for $n\geq 3$ is resolvable.

A singular quotient $3$-manifold is a quotient space of a topological $3$-manifold by a continuum that generates a singular point. An inverse limit of closed $3$-manifolds is a spa…

Let $X$ be a resolvable generalized manifold. A codimension-one manifold factor is a space such that $X\times\mathbb R$ is a topological manifold. Moore conjecture. Every resolvabl…

Let $X$ be a generalized $n$-manifold with $n\geq 7$ satisfying the disjoint disks property. Bryant–Ferry–Mio–Weinberger conjecture. The space $X$ is homogeneous. If true, this wou…

Let $X$ be a generalized $n$-manifold with $n\geq 3$. Generalized manifolds resolution conjecture. The space $X$ has a resolution. The conjecture is false in higher dimensions: non…