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

Abstract

In this paper, we consider discrete groups in ${\mathrm{PGL}}_d(\mathbb{R})$ 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 $\mathrm{CAT}(0)$ spaces.

Minor revisions, to appear in the Journal of the London Mathematical Society. 20 pages. Comments welcome