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

## TL;DR

This paper extends the flat torus theorem to convex co-compact groups acting on convex domains in real projective space, providing new insights into their geometric structure.

## Contribution

It introduces an analogue of the flat torus theorem for convex co-compact actions of projective linear groups, bridging a gap in geometric group theory.

## Key findings

- Established a flat torus theorem analogue for convex co-compact groups in projective space
- Demonstrated geometric properties of discrete groups acting on convex domains
- Provided tools for analyzing the structure of convex co-compact actions

## Abstract

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.