7 problems

Homogeneity conjecture. Every connected generalized $n$-manifold with the disjoint disks property is homogeneous, for $n\geq 5$.

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 an $(n\geq 5)$-dimensional Busemann $G$-space. Busemann $G$-spaces resolution conjecture. The space $X$ has a resolution. The conjecture is related to the unresolved hig…

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…