Bounded projections to the $\mathcal{Z}$-factor graph

Matt Clay, Caglar Uyanik

Suppose $G$ is a free product $G=A_1\ast A_2\ast \cdots \ast A_k\ast F_N$, where each of the groups $A_i$ is torsion-free and $F_N$ is a free group of rank $N$. Let $\mathcal{O}$ be the de…