8 problems

The Bieri–Stallings connectivity-at-infinity conjecture. For $n\geq 2$, the group $B_n$ is $(n-2)$-connected at infinity.

Let $G$ be an infinite primitive permutation group whose subdegrees are all finite, and let $(m_r)$ be its lower subdegree sequence. Permutation-ends conjecture. If $(m_r)$ grows e…

Specker's knot-space covering conjecture. The conjecture that the knot space $\mathbb S^3-K$ is aspherical is equivalent to the conjecture that the knot group…

The one-ended subgroup characterization. The subgroup $H$ of the finitely generated group $G$ is 1-ended in $G$ if and only if for each splitting $A\ast_C B$ of $G$, where…

Let $G$ be a finitely presented group. Geoghegan–Mihalik's conjecture. The group $G$ is semistable at infinity. This conjecture extends the semistability result for hyperbolic grou…

P3R–telescopic-type conjecture. The class of properly $3$-realizable groups and the class of groups of telescopic type at each end are the same.

A group is semistable at infinity if, for a proper, 1-ended space on which it acts geometrically, any two geodesic rays are properly homotopic. A group is CAT(0) if it acts geometr…

Let a P3R group be a finitely presented group whose universal cover is proper homotopy equivalent to a 3-manifold. An end is semi-stable when its fundamental pro-group at infinity…