Codimension-$1$ Simplices in Divisible Convex Domains

DOI10.2140/GT.2021.25.3725arXiv2001.11096MaRDI QIDQ6333756

Publication date: 29 January 2020

Abstract: Properly embedded simplices in a convex divisible domain

O m e g a s u b s e t m a t h b b R e x t r m 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.

Mathematics Subject Classification ID

Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) General geometric structures on low-dimensional manifolds (57M50) Geometric structures on manifolds of high or arbitrary dimension (57N16)

This page was built for publication: Codimension-$1$ Simplices in Divisible Convex Domains

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6333756)