8 problems

Nonexistence conjecture. There is no example of a manifold of type 4.

A graph of $\mathbb{Z}^2$ has two vertex orbits whose stabilizers satisfy the relevant inclusion, with the first orbit intended for elimination by a sequence of moves. Non-eliminab…

Let $L$ be an $n$-component prime link whose complement has only hyperbolic pieces. Let $\vec M=(M_1,\ldots,M_n)$ be a coloring, with limiting ratios…

Let $\Gamma$ be a one-ended hyperbolic group that is not Fuchsian. Its JSJ decomposition is the canonical graph-of-groups decomposition over two-ended subgroups, with vertex groups…

Let $G$ be a finitely presented group. A JSJ-decomposition over the class of its $VPC(n+1)$ subgroups is a JSJ-decomposition whose edge groups belong to that class, and a vertex gr…

Let $G$ be a one-relator group with torsion that does not admit a free group as a free factor. Since one-relator groups with torsion are hyperbolic, $G$ has a JSJ-decomposition, me…

A one-relator group with torsion is a group with a presentation $G=\langle X;R^n\rangle$, where $R$ is not a proper power and $n>1$. Pride's folk conjecture. Apart from the complic…

Let $F$ be the free group appearing in the free product $F*\langle x,y\rangle$. A quotient is fully residually $F$ if it has the residual property relative to $F$, and its JSJ deco…