5 problems

Fixed-point conjecture. Every locally elliptic action of a finitely generated group on a finitely dimensional nonpositively curved complex has a global fixed point. In particular,…

Small cancellation torsion subgroup conjecture. Every torsion subgroup of $G$ is finite.

Let $G$ be a finitely generated group defined by an infinite presentation satisfying the small cancellation condition $C'(1/10)$. Weak amenability and $C^*$-exactness (equivalently…

Kapovich–Weidmann higher-stabilization conjecture. For every $1\le t<m$, the generating $(k+t)$-tuple $(a_1,\ldots,a_k,1,\ldots,1)$ is not equivalent to a $(k+t)$-tuple of type…

Kapovich–Weidmann stabilization conjecture. In the above construction, at least $k$ stabilizations are needed to make the tuples $(a_1,\ldots,a_k)$ and $(b_1,\ldots,b_k)$ Nielsen e…