Bounded diagonal orbits in homogeneous spaces over function fields

This paper is about topological rigidity of diagonal group actions on the homogeneous ${\text{SL}}_4(\text{F}(\text{\hspace{0.17em}⁣}(t^{-1})\text{\hspace{0.17em}⁣}))\mathrm{/}{\text{SL}}_4(\text{F}[t])$ where $\text{F}$ is a finite field of characteristic $3$. We show that there is a non-closed relatively compact orbit of the diagonal group.