Cubical small-cancellation quotients of non-products

Macarena Arenas, Kasia Jankiewicz, Daniel T. Wise

We show that if $X$ is a compact nonpositively curved cube complex which is a non-product, then $\ddot{I}{€}_{1}X$ has a proper quotient that is $\ddot{I}{€}_1$ of a cube complex with these same prop…