#### Volume 25, issue 7 (2021)

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Codimension-$1$ simplices in divisible convex domains

### Martin D Bobb

Geometry & Topology 25 (2021) 3725–3753
##### Abstract

Properly embedded simplices in a convex divisible domain $\Omega \subset ℝ{P}^{d}$ behave somewhat like flats in Riemannian manifolds (Geom. Dedicata 33 (1990) 251–263), so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $\left(d-1\right)$–tori in the compact quotient manifold. If this collection of virtual tori is nonempty, then the components of its complement are cusped convex projective manifolds with type $d$ cusps.

##### Keywords
geometry, low-dimensional topology, divisible domains, Benoist manifolds, real projective geometry
##### Mathematical Subject Classification
Primary: 57M50
Secondary: 20H10, 57N16