Codimension-$1$ Simplices in Divisible Convex Domains

Abstract

Properly embedded simplices in a convex divisible domain $\Omega \subset \mathbb{R}{\text{P}}^d$ behave somewhat like flats in Riemannian manifolds, so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $(d-1)$-tori in the compact quotient manifold. If this collection of virtual tori is non-empty, then the components of its complement are cusped convex projective manifolds with type $d$ cusps.

21 pages, 3 figures

References in corpus (1)

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

Cited by in corpus (2)

• Convex co-compact actions of relatively hyperbolic groups
• Topological mixing of the geodesic flow on convex projective manifolds