A flat torus theorem for convex co‐compact actions of projective linear groups

In this paper, we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish an analogue of the well known flat torus theorem for ${\rm CAT}(0)$ spaces.
Minor revisions, to appear in the Journal of the London Mathematical Society. 20 pages. Comments welcome