Codimension-1 simplices in divisible convex domains

Bobb, Martin D

doi:10.2140/gt.2021.25.3725

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Codimension-$1$ simplices in divisible convex domains

Martin D Bobb

Geometry & Topology 25 (2021) 3725–3753

DOI: 10.2140/gt.2021.25.3725

Abstract

Properly embedded simplices in a convex divisible domain $Ω \subset ℝ P^{d}$ 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 $(d - 1)$ –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

References

Publication

Received: 22 June 2020

Revised: 17 September 2020

Accepted: 23 October 2020

Published: 25 January 2022

Proposed: Ian Agol

Seconded: David M Fisher, Anna Wienhard

Authors

Martin D Bobb
Department of Mathematics The University of Texas at Austin Austin, TX United States	Department of Mathematics University of Michigan Ann Arbor, MI United States

Volume 25, issue 7 (2021)