# Quasi-isometric rigidity of certain products of groups

Let $G_1,G_2$ be two delta-hyperbolic groups. If $G_1\times \Bbb{Z}$ is quasi-isometric to $G_2\times \Bbb{Z}$, must it be true that $G_1$ is quasi-isometric to $G_2$?

This is similar to the classic topology problem where crossing two non-homeomorphic spaces with $\Bbb{R}$ can create two homeomorphic spaces which are homeomorphic.

• Yes, this is proven in our papers with Leeb and Kleiner. – Misha Nov 26 '13 at 20:43