2 problems

Acylindrical vertex-pair conjecture. Either $s_i=1$ (and hence $s_j=1$), or $i=j$ and $g^{-1}H_rg=H_r$.

Let $\Gamma$ be a colorable HHG. A quasitree of metric spaces and a projection complex are associated to $\Gamma$ using the constructions of Bestvina–Bromberg–Fujiwara. Assume eith…